In a triangle PQR, PQ = PR and PT is perpendicular to QR. If PQ = 17 cm and PT = 15 cm, then what is the length of QR in cm?

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Accepted Answer

Given triangle PQR with PQ = PR, so it is isosceles with P as the apex. PT is perpendicular to QR, so T is the midpoint of QR because in an isosceles triangle, the altitude from the apex bisects the base.

Let QR = x cm, then QT = TR = x/2 cm.

In right triangle PTQ:  
PT^2 + QT^2 = PQ^2  
=> 15^2 + (x/2)^2 = 17^2  
=> 225 + x^2/4 = 289  
=> x^2/4 = 289 - 225 = 64  
=> x^2 = 256  
=> x = 16 cm

Therefore, the length of QR is 16 cm.

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