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

A

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.