Question

Right triangles MNP and QRS are congruent.

Right triangles M N P and Q R S are shown. The length of side Q S is 8 meters. The length of M N is 17 meters and the length of P N is 15 meters.

What is the area of △MNP?

40 m2
60 m2
68 m2
127.5 m2

Answer 1

Because the triangles are congruent in the order M↔Q, N↔R, P↔S, segment QS corresponds to MP, so MP = 8 m. MN = 17 m and PN = 15 m; 8^2 + 15^2 = 64 + 225 = 289 = 17^2, so the legs are 8 and 15. Area = (1/2)(8)(15) = 60 m^2.

Answer: 60 m^2.