Q:

Which set of side lengths form a right triangle?A.10 cm, 6 cm, 8 cmB.3 ft, 6 ft, 5 ftC.14 m, 20 m, 25 m.D.7 cm, 8 cm, 10 cm

Accepted Solution

A:
Answer:AStep-by-step explanation:To form a right triangle, the legs of a triangle must satisfy the Pythagorean theorem: [tex]a^{2}+b^{2}= c^{2}[/tex]. We will test each triangle using a as the smallest side, b as the next smallest and c as the largest side.A. [tex]a^{2}+b^{2}= c^{2}  \\6^{2}+8^{2}= 10^{2}  \\36+64=100\\100=100[/tex]This is a right triangle.B. [tex]a^{2}+b^{2}= c^{2}  \\3^{2}+5^{2}= 6^{2}  \\9+25=36\\34=36[/tex]This is not a right triangle.C. [tex]a^{2}+b^{2}= c^{2}  \\14^{2}+20^{2}= 125^{2}  \\196+400=625\\596=625[/tex]This is not a right triangle.D. [tex]a^{2}+b^{2}= c^{2}  \\7^{2}+8^{2}= 10^{2}  \\49+64=100\\113=100[/tex]This is not a right triangle.