Question

In the following figure, find the sides marked x and y.

Answer 1

Given,

∆SQR is right angle triangle, right angle at Q.

Here base (QR) = 60

Hypotenuse (SR) = 61

Perpendicular (SQ) = x = ?

To find SQ, apply Pythagoras theorem in ∆SQR.

SR² = SQ² + QR²

61² + x² + 60²

x² = 3721 – 3600

x = `sqrt(121)`

x = 11

Thus, SQ = x = 11

Now, ∆PQR is right angle triangle, right angle at Q.

Here base (QR) = 60

Hypotenuse (QP) = y = ?

Perpendicular (PQ) = PS + SQ = 69 + x = 69 + 11 = 80

Apply Pythagoras theorem in ∆PQR.

PR² = PQ² + QR²

y² = 80² + 60²

y² = 6400 + 3600

y = `sqrt(10000)`

y = 100

Thus, PR = y = 100

Hence, x = 11, y = 100.