In the given figure, angle Q is a right angle. PS : QS = 3 : 1, RT : QT = 5 : 2, and PU : UR = 1 : 1. If the area of tri...

Question

In the given figure, angle Q is a right angle. PS : QS = 3 : 1, RT : QT = 5 : 2, and PU : UR = 1 : 1. If the area of triangle QTS is 20 cm^2, then the area of triangle PQR in cm^2 is ______.

Accepted Answer

Area of triangle PQR = 280 cm^2 Triangle PQR has a right angle at Q. Points S on PQ, T on QR, and U on PR are defined by given ratios. We are told the area of small triangle QTS and must find the area of the full triangle PQR. The key insight is that since angle Q = 90 degrees, the areas are related directly by the product of the ratio of the two legs through Q.