Basic Geometric Concepts - Problems on Triangles for Exams

Basic Geometric Concepts - Problems on Triangles - Case Studies

Q. If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE are 4 cm and 8 cm respectively, what is the ratio of the areas of the triangles?

A. 1:2
B. 1:4
C. 2:1
D. 4:1

Solution

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (4/8)^2 = (1/2)^2 = 1/4.

Correct Answer: B — 1:4

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Q. In triangle PQR, if PQ = 8 cm, QR = 6 cm, and PR = 10 cm, what type of triangle is it?

A. Equilateral
B. Isosceles
C. Scalene
D. Right

Solution

Since all sides are of different lengths, triangle PQR is a scalene triangle.

Correct Answer: C — Scalene

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Q. In triangle XYZ, if angle X is 30 degrees and angle Y is 60 degrees, what is angle Z?

A. 30 degrees
B. 60 degrees
C. 90 degrees
D. 120 degrees

Solution

The sum of the angles in a triangle is 180 degrees. Therefore, angle Z = 180 - (30 + 60) = 90 degrees.

Correct Answer: C — 90 degrees

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Q. What is the perimeter of an equilateral triangle with a side length of 6 cm?

A. 12 cm
B. 18 cm
C. 24 cm
D. 30 cm

Solution

The perimeter of an equilateral triangle is given by P = 3 * side length = 3 * 6 = 18 cm.

Correct Answer: B — 18 cm

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Basic Geometric Concepts - Problems on Triangles - Case Studies

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