Basic Geometric Concepts - Applications for Competitive Exams

Basic Geometric Concepts - Applications

Q. If two angles of a triangle are 45 degrees and 55 degrees, what is the measure of the third angle?

A. 80 degrees
B. 90 degrees
C. 100 degrees
D. 70 degrees

Solution

Third angle = 180 - (45 + 55) = 80 degrees.

Correct Answer: A — 80 degrees

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Q. Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what is the length of the corresponding side in the second triangle if its longest side is 10 cm?

A. 6 cm
B. 8 cm
C. 10 cm
D. 12 cm

Solution

The ratio of the sides is 10/5 = 2. Therefore, the corresponding side is 4 * 2 = 8 cm.

Correct Answer: B — 8 cm

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Q. Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what is the length of the longest side of the second triangle if its shortest side is 6 cm?

A. 8 cm
B. 10 cm
C. 12 cm
D. 9 cm

Solution

The ratio of the sides is 6/3 = 2. Therefore, the longest side is 5 * 2 = 10 cm.

Correct Answer: B — 10 cm

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Q. What is the distance between the points (3, 4) and (7, 1) in the coordinate plane?

A. 5
B. 4
C. 3
D. 6

Solution

Distance = √((7-3)² + (1-4)²) = √(4 + 9) = √13 ≈ 3.6.

Correct Answer: A — 5

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Q. What is the length of the diagonal of a rectangle with a length of 6 cm and a width of 8 cm?

A. 10 cm
B. 12 cm
C. 14 cm
D. 16 cm

Solution

Diagonal = √(length² + width²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Correct Answer: A — 10 cm

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Q. What is the length of the hypotenuse of a right triangle with legs of 3 cm and 4 cm?

A. 5 cm
B. 7 cm
C. 6 cm
D. 8 cm

Solution

Using Pythagorean theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

Correct Answer: A — 5 cm

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Q. What is the perimeter of a rectangle with a length of 8 cm and a width of 3 cm?

A. 22 cm
B. 24 cm
C. 20 cm
D. 26 cm

Solution

Perimeter = 2(length + width) = 2(8 + 3) = 22 cm.

Correct Answer: A — 22 cm

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Q. What is the volume of a cylinder with a radius of 3 cm and a height of 5 cm?

A. 45π cm³
B. 30π cm³
C. 60π cm³
D. 15π cm³

Solution

Volume = πr²h = π * 3² * 5 = 45π cm³.

Correct Answer: A — 45π cm³

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Basic Geometric Concepts - Applications

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