Theory question 108
Mensuration of Plane Shapes(a) In ΔPQR, ∠PQR = 90°. If its area is 216 cm2 and |PQ| : |QR| is 3 : 4, find |PR|.
(b) The present ages of a man and his son are 47 years and 17 years respectively. In how many years would the man's age be twice that of his son?
Show the model answer
Model answer
(a) Let PQ = 3k, QR = 4k: ½ × 3k × 4k = 216 → 6k2 = 216 → k = 6
PQ = 18 cm, QR = 24 cm
|PR| = √(182 + 242) = 30 cm
(b) 47 + n = 2(17 + n) → 47 + n = 34 + 2n
n = 13 years
Explanation
The right angle is at Q, so PQ and QR are the base and height.