Similarity and Trigonometry Basics for Competitive Exams

Similarity and Trigonometry Basics - Proof-based Questions - Case Studies

Q. If triangle DEF is similar to triangle XYZ and the length of DE is 6 cm, what is the length of XY if the ratio of similarity is 2:3?

Solution

Using the ratio of similarity, if DE = 6 cm, then XY = (3/2) * 6 = 9 cm.

Correct Answer: C — 9 cm

Q. In triangle PQR, if PQ = 8 cm, PR = 6 cm, and angle P = 90 degrees, what is the length of QR?

Solution

Using the Pythagorean theorem, QR = √(PQ² + PR²) = √(8² + 6²) = √(64 + 36) = √100 = 10 cm.

Correct Answer: A — 10 cm

Q. What is the length of the radius of a circle if the area is 50π square units?

Solution

Area of a circle = πr². Setting 50π = πr² gives r² = 50, so r = √50 = 5√2 ≈ 7.07 units.

Correct Answer: B — 10 units

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