Question

In the figure, ΔPQR is right angled at Q, seg QS ⊥ seg PR. Find x, y.

Answer 1

Given: ΔPQR = 90°, seg QS ⊥ seg PR.

According to the geometric mean theorem,

QS² = PS × RS

or QS = `sqrt(PS xx RS)`

= `sqrt(10 xx 8)`

= `sqrt(2 xx 5 xx 2 xx 2 xx 2)`

= `4sqrt(5)`

In ΔQRS, by Pythagoras theorem,

QS² = QS² + SR² 

= `(4sqrt(5))^2 + (8)^2`

= 80 + 64

= 144

⇒ QR = `sqrt(144)` = 12

Hence, x = `4sqrt(5)`, y = 12.