Question

Which of the following measurements of trapeziums PQRS with PQ||RS are suitable for its construction?

• A. PQ = 8 cm, QR = 3 cm, RS = 5 cm, ∠P = 50^o and ∠S = 130^o
• B. PQ = 9 cm, QR = 7 cm, RS = 5.5 cm, ∠P = 80^o and ∠S = 110^o
• C. PQ = 6 cm, QR = 4 cm, RS = 2 cm, ∠Q = 65^o and ∠R = 115^o
• D. PQ = 7.5 cm, QR = 5 cm, RS = 4 cm, ∠Q = 40^o and R = 120^o

Answer 1

The correct option is C

PQ = 6 cm, QR = 4 cm, RS = 2 cm, ∠Q = 65^o and ∠R = 115^o

A trapezium can be constructed uniquely if the measurement of three sides and two included angles are given. Also, as PQ||RS, we should have ∠R + ∠Q = 180^o.

Now, the trapezium PQRS with given measurements PQ = 6 cm, QR = 4 cm, RS = 2 cm, ∠Q = 65^o and ∠R = 115^o can be constructed uniquely.