Q. If the lengths of two sides of a triangle are 8 cm and 6 cm, what is the range of possible lengths for the third side?
A.
2 cm to 14 cm
B.
2 cm to 10 cm
C.
4 cm to 14 cm
D.
4 cm to 10 cm
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Solution
The length of the third side must be greater than the difference of the other two sides and less than their sum: |8 - 6| < third side < 8 + 6, which gives 2 < third side < 14.
Correct Answer:
B
— 2 cm to 10 cm
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Q. In a right triangle, if one leg is 6 cm and the other leg is 8 cm, what is the length of the hypotenuse?
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
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Solution
Using the Pythagorean theorem: hypotenuse = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. In an equilateral triangle, if one side measures 12 cm, what is the area of the triangle?
A.
36√3 cm²
B.
24 cm²
C.
48 cm²
D.
144 cm²
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Solution
The area of an equilateral triangle is given by the formula: Area = (√3/4) * side² = (√3/4) * 12² = 36√3 cm².
Correct Answer:
A
— 36√3 cm²
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Q. In an isosceles triangle, if the equal sides are each 10 cm and the base is 12 cm, what is the height of the triangle?
A.
8 cm
B.
6 cm
C.
5 cm
D.
4 cm
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Solution
Using the Pythagorean theorem, the height can be found by splitting the triangle in half: height = √(10^2 - 6^2) = √(100 - 36) = √64 = 8 cm.
Correct Answer:
B
— 6 cm
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Q. What is the length of the altitude from the vertex of a triangle to the base if the area is 40 cm² and the base is 10 cm?
A.
4 cm
B.
6 cm
C.
8 cm
D.
10 cm
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Solution
Using the area formula: Area = 1/2 * base * height, we can rearrange to find height: height = (2 * Area) / base = (2 * 40) / 10 = 8 cm.
Correct Answer:
B
— 6 cm
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Q. What is the length of the altitude from the vertex of a triangle with a base of 10 cm and an area of 40 cm²?
A.
4 cm
B.
6 cm
C.
8 cm
D.
10 cm
Show solution
Solution
Using the area formula: Area = 1/2 * base * height, we can solve for height: 40 = 1/2 * 10 * height, so height = 8 cm.
Correct Answer:
B
— 6 cm
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Q. What is the length of the altitude from the vertex of a triangle with a base of 10 cm and an area of 30 cm²?
A.
3 cm
B.
5 cm
C.
6 cm
D.
8 cm
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Solution
Using the area formula: Area = 1/2 * base * height, we can solve for height: 30 = 1/2 * 10 * height, so height = 30 / 5 = 6 cm.
Correct Answer:
B
— 5 cm
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Q. What is the length of the median from vertex A to side BC in triangle ABC with sides AB = 6 cm, AC = 8 cm, and BC = 10 cm?
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
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Solution
The length of the median can be calculated using the formula: median = 1/2 * √(2AB^2 + 2AC^2 - BC^2) = 1/2 * √(2*6^2 + 2*8^2 - 10^2) = 7 cm.
Correct Answer:
C
— 7 cm
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Q. What is the perimeter of a triangle with sides measuring 7 cm, 10 cm, and 5 cm?
A.
20 cm
B.
22 cm
C.
24 cm
D.
26 cm
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Solution
The perimeter of a triangle is the sum of the lengths of its sides: 7 + 10 + 5 = 22 cm.
Correct Answer:
B
— 22 cm
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Q. What is the perimeter of a triangle with sides measuring 7 cm, 5 cm, and 3 cm?
A.
10 cm
B.
12 cm
C.
15 cm
D.
20 cm
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Solution
The perimeter of a triangle is the sum of its sides: 7 + 5 + 3 = 15 cm.
Correct Answer:
C
— 15 cm
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