Q. In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the length of side AB?
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Solution
Length of AB = √[(4-1)² + (6-2)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.
Correct Answer:
B
— 5
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Q. In triangle ABC, if the lengths of sides a = 10, b = 24, and angle C = 60 degrees, find the length of side c.
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Solution
Using the cosine rule: c^2 = a^2 + b^2 - 2ab*cos(C) = 10^2 + 24^2 - 2*10*24*(1/2) = 100 + 576 - 240 = 436. Thus, c = √436 = 20.
Correct Answer:
A
— 20
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Q. In triangle ABC, if the lengths of sides a, b, and c are 5, 12, and 13 respectively, what is the perimeter of the triangle?
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Solution
Perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer:
B
— 25
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Q. In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 7² + 24² = 49 + 576 = 625 = 25², triangle ABC is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what is the area of the triangle?
A.
84
B.
96
C.
120
D.
168
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Solution
Using Heron's formula, s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84.
Correct Answer:
B
— 96
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Q. In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectively, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 8² + 15² = 17², triangle ABC is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle ABC, if the lengths of sides are 8 cm, 15 cm, and 17 cm, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Isosceles
Show solution
Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle ABC, if the lengths of the sides are 10 cm, 24 cm, and 26 cm, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 10² + 24² = 100 + 576 = 676 = 26², triangle ABC is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle ABC, if the lengths of the sides are 5, 12, and 13, what is the perimeter?
Show solution
Solution
Perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer:
B
— 25
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Q. In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, what is the perimeter?
A.
30 cm
B.
40 cm
C.
50 cm
D.
60 cm
Show solution
Solution
Perimeter = 8 + 15 + 17 = 40 cm.
Correct Answer:
A
— 30 cm
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Q. In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the area of the triangle?
A.
60
B.
80
C.
120
D.
150
Show solution
Solution
Using Heron's formula, the semi-perimeter s = (8 + 15 + 17)/2 = 20. Area = √[s(s-a)(s-b)(s-c)] = √[20(20-8)(20-15)(20-17)] = √[20*12*5*3] = 60.
Correct Answer:
A
— 60
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Q. In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle ABC, if the lengths of the sides are a = 5, b = 12, and c = 13, what is the perimeter of the triangle?
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Solution
The perimeter of a triangle is the sum of its sides. Therefore, perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer:
B
— 25
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Q. In triangle ABC, if the lengths of the sides are a = 8, b = 15, and c = 17, what is the value of cos A?
A.
0.5
B.
0.6
C.
0.8
D.
0.9
Show solution
Solution
Using the cosine rule, cos A = (b² + c² - a²) / (2bc) = (15² + 17² - 8²) / (2 * 15 * 17) = 0.8.
Correct Answer:
C
— 0.8
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Q. In triangle ABC, if the lengths of the sides are a = 8, b = 15, and c = 17, what is the perimeter?
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Solution
The perimeter of a triangle is the sum of its sides: a + b + c = 8 + 15 + 17 = 40.
Correct Answer:
A
— 30
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Q. In triangle ABC, if the lengths of the sides are in the ratio 3:4:5, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since the sides are in the ratio of a Pythagorean triplet (3, 4, 5), triangle ABC is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle ABC, if the sides are in the ratio 3:4:5, what is the nature of the triangle?
A.
Equilateral
B.
Isosceles
C.
Right
D.
Scalene
Show solution
Solution
The sides satisfy the Pythagorean theorem, hence it is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle ABC, if the sides are in the ratio 3:4:5, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.
Correct Answer:
C
— Right
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Q. In triangle MNO, if angle M = 45 degrees and angle N = 45 degrees, what is angle O?
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
Angle O = 180 - (angle M + angle N) = 180 - (45 + 45) = 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. In triangle PQR, if PQ = 10 cm, QR = 24 cm, and PR = 26 cm, what is the area of the triangle?
A.
120 cm²
B.
120√3 cm²
C.
240 cm²
D.
48 cm²
Show solution
Solution
Using Heron's formula, s = (10 + 24 + 26)/2 = 30. Area = √(30(30-10)(30-24)(30-26)) = √(30*20*6*4) = 120 cm².
Correct Answer:
A
— 120 cm²
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Q. In triangle XYZ, if XY = 8 cm, YZ = 15 cm, and XZ = 17 cm, is it a right triangle?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if XY is the hypotenuse
Show solution
Solution
Since 8^2 + 15^2 = 17^2, triangle XYZ is a right triangle.
Correct Answer:
A
— Yes
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Q. The area of triangle ABC is 24 cm², and the base BC = 8 cm. What is the height from A to BC?
A.
6 cm
B.
8 cm
C.
4 cm
D.
3 cm
Show solution
Solution
Area = 1/2 * base * height => 24 = 1/2 * 8 * height => height = 6 cm.
Correct Answer:
A
— 6 cm
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Q. The area of triangle ABC is 30 square units, and the base BC is 10 units. What is the height from A to BC?
A.
3 units
B.
6 units
C.
5 units
D.
4 units
Show solution
Solution
Area = 1/2 * base * height => 30 = 1/2 * 10 * height => height = 6 units.
Correct Answer:
B
— 6 units
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Q. The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. What type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 7^2 + 24^2 = 25^2, triangle ABC is a right triangle.
Correct Answer:
C
— Right
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Q. What is the area of an equilateral triangle with side length 'a'?
A.
(√3/4)a²
B.
(1/2)a²
C.
(√2/2)a²
D.
(3/2)a²
Show solution
Solution
The area of an equilateral triangle is given by the formula (√3/4)a².
Correct Answer:
A
— (√3/4)a²
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Q. What is the circumradius of a triangle with sides 5, 12, and 13?
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Solution
For a right triangle, the circumradius R = hypotenuse/2 = 13/2 = 6.5.
Correct Answer:
B
— 7
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Q. What is the circumradius of a triangle with sides 6, 8, and 10?
Show solution
Solution
Circumradius R = (abc)/(4K), where K is the area. Area K = 24 (using Heron's formula). R = (6*8*10)/(4*24) = 5.
Correct Answer:
A
— 5
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Q. What is the circumradius of a triangle with sides 7, 24, and 25?
A.
12.5
B.
13
C.
14
D.
15
Show solution
Solution
The circumradius R of a triangle can be calculated using the formula R = (abc)/(4 * Area). Here, Area = 84 cm², so R = (7 * 24 * 25)/(4 * 84) = 13.
Correct Answer:
B
— 13
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Q. What is the circumradius of an equilateral triangle with side length a?
A.
a/√3
B.
a/2
C.
a/√2
D.
a/√3
Show solution
Solution
The circumradius R of an equilateral triangle is given by R = a/(√3).
Correct Answer:
D
— a/√3
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Showing 31 to 60 of 67 (3 Pages)
Properties of Triangles MCQ & Objective Questions
The "Properties of Triangles" is a fundamental topic in geometry that plays a crucial role in various school and competitive exams. Understanding these properties not only enhances your conceptual clarity but also boosts your confidence in tackling MCQs and objective questions. Regular practice with these important questions can significantly improve your exam performance and help you score better.
What You Will Practise Here
Types of triangles: Equilateral, Isosceles, and Scalene
Triangle inequality theorem and its applications
Sum of angles in a triangle and its implications
Properties of congruence and similarity in triangles
Key formulas related to area and perimeter of triangles
Understanding medians, altitudes, and angle bisectors
Diagrams illustrating key concepts for better visualization
Exam Relevance
The topic of "Properties of Triangles" is frequently tested in CBSE, State Boards, and competitive exams like NEET and JEE. You can expect questions that assess your understanding of triangle properties, including multiple-choice questions that require you to apply theorems and formulas. Common question patterns include identifying types of triangles, solving for unknown angles, and applying the triangle inequality theorem.
Common Mistakes Students Make
Confusing the properties of different types of triangles
Misapplying the triangle inequality theorem
Overlooking the importance of diagrams in solving problems
Neglecting to check for congruence and similarity conditions
FAQs
Question: What is the triangle inequality theorem?Answer: The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Question: How do I find the area of a triangle?Answer: The area of a triangle can be calculated using the formula: Area = 1/2 × base × height.
Now is the time to enhance your understanding of triangles! Dive into our practice MCQs and test your knowledge on the important Properties of Triangles questions for exams. Start solving today and see the difference in your preparation!
