Question

In ΔPQR, PS ⊥ QR. Find the sides marked a and b if PR = 41 cm, QS = 12 cm and SR = 40 cm.

Answer 1

Given,

In ΔPQR,

As PS is perpendicular.

ΔPSR is right angle triangle, right angle at S.

Here Base (SR) = 40 cm

Hypotenuse (PR) = 41 cm

Perpendicular (PS) = a = ?

To find PS, apply Pythagoras theorem in ΔPSR

(PR)² = (SR)² + (PS)²

(41)² = (40)² + a²

a² = 1681 – 1600

a = `sqrt(81)`

a = 9

Thus, PS = a = 9 cm

Now, ΔPSQ is right angle triangle, right angle at S.

Here Base (SQ) = 12 cm

Hypotenuse (QP) = ?

Perpendicular (PS) = 9 cm

Apply Pythagoras theorem in ΔPSQ.

(QP)² = (SQ)² + (PS)²

b² = (12)² + (9)²

b² = 144 + 81

b = `sqrt(225)`

b = 15

Thus, QP = b = 15 cm

Hence, a = 9 cm, b = 15 cm.