if the area of triangle PQR be 150 cm2, angle P = 90 , side PQ = x cm and - Maths - Surface Areas and Volumes

Question

if the area of triangle PQR be 150 cm2, angle P = 90 , side PQ = x
cm and PR = ( x+5) cm, find all the sides of the triangle ?

Nishima Pasricha · Accepted Answer

Dear student,

Area of △PQR=12×RP×PQ⇒150=12×x+5x⇒300=x2+5x⇒x2+5x-300=0⇒x2+20x-15x-300=0⇒xx+20-15x+20=0⇒x-15x+20=0⇒x=15, -20Side cannot be negative
 Therefore, x=15 cmPQ=15 cm, PR=20 cmBy pythagoras theorem, 152+202=RQ2RQ2=625⇒RQ=25 cm
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if the area of triangle PQR be 150 cm2, angle P = 90 , side PQ = x cm and PR = ( x+5) cm, find all the sides of the triangle ?