Question

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

Answer 1

Given:

△PQR is right-angled at Q.

QS ⊥ PR

In the diagram:

PS = x

SR = 8

QR = y

(QS)² = PS ⋅ SR

But QS is perpendicular, forming two smaller similar triangles.

Let altitude be QS = h

h² = x ⋅ 8     ...(1)

For the leg QR = y:

(QR)² = SR ⋅ PR

PR = PS + SR = x + 8

y² = 8(x + 8)     ...(2)

Since the image shows that QS = 4 (length of altitude), we substitute:

4² = x ⋅ 8

16 = 8x

x = 2

Put x = 2 in (2):

y² = 8(2 + 8)

y² = 8 ⋅ 10 = 80

y = `sqrt80`

`= 4sqrt5`