Question

In the given figure, PQ and TS are perpendiculars to QS. R is the mid-point of QS and ∠PRT = 90°. If PQ = 9 cm, QS = 24 cm, TS = 16 cm, find PT.

Answer 1

Given,

In the given figure, PQ and TS are perpendiculars to QS.

R is the mid-point of QS and ∠PRT = 90°.

If PQ = 9 cm, QS = 24 cm, TS = 16 cm.

ΔPQR is right angle triangle, right angle at Q.

Here base (QR) = `(QS)/2` cm = `24/2` cm = 12 cm

Hypotenuse (PR) = ?

Perpendicular (PQ) = 9 cm

To find PR, apply Pythagoras theorem in ∆PQR.

PR² = PQ² + QR²

PR² = 9² + 12²

PR² = 81 + 144

PR = `sqrt(225)`

PR = 15

Now, ∆TSR is right angle triangle, right angle at S.

Here base (RS) = `(QS)/2` cm = `24/2` cm = 12 cm

Hypotenuse (TR) = ?

Perpendicular (TS) = 16 cm

Apply Pythagoras theorem in ∆TSR.

TR² = TS² + RS²

TR² = 16² + 12²

TR² = 256 + 144

TR = `sqrt(400)`

TR = 20

Join PT, △PRT is right angle triangle, right angle at R.

Applying Pythagoras theorem.

PT² = PR² + TR²

PT² = 15² + 20²

PT² = 225 + 400

PT² = 625

PT = `sqrt(225)`

PT = 25 cm

Hence, PT = 25 cm