Question

Which of the following are right triangles? Check all that apply.

A. A triangle with side lengths 6 inches, 8 inches, 10 inches
B. A triangle with side lengths 8, 15, 17
C. A triangle with side lengths 5, 12, 13
D. A triangle with side lengths 4, 5, 6

Please explain answer. Is there a way to solve this or ratios to remember?

Thank you!

Answer 1

Given a triangle with side lengths a,b,c. The length c is the longest side

If you can show that a^2 + b^2 = c^2 is true, then the triangle is a right triangle. This is the converse of the pythagorean theorem.

Answer 2

Example

a = 3
b = 4
c = 5

a^2 + b^2 = c^2
3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25

the triangle with sides 3,4,5 is a right triangle