Question

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

Answer 1

Answer:

A

Step-by-step explanation:

To form a right triangle, the legs of a triangle must satisfy the Pythagorean theorem: $a^{2}+b^{2}= c^{2}$. We will test each triangle using a as the smallest side, b as the next smallest and c as the largest side.

A. $a^{2}+b^{2}= c^{2}  \\6^{2}+8^{2}= 10^{2}  \\36+64=100\\100=100$

This is a right triangle.

B. $a^{2}+b^{2}= c^{2}  \\3^{2}+5^{2}= 6^{2}  \\9+25=36\\34=36$

This is not a right triangle.

C. $a^{2}+b^{2}= c^{2}  \\14^{2}+20^{2}= 125^{2}  \\196+400=625\\596=625$

This is not a right triangle.

D. $a^{2}+b^{2}= c^{2}  \\7^{2}+8^{2}= 10^{2}  \\49+64=100\\113=100$

This is not a right triangle.