Question

Below are the lengths of the sides of a triangle. Which is a right triangle?

a. 9,8,6
b. 10,8,7
c.6,8,10
d. none
e. 9,8,7

Answer 1

c. 6, 8, 10

Explanation:

In order for three side lengths of a triangle to be a right triangle, they have to satisfy the Pythagorean theorem, which is given by:

a^2 + b^2 = c^2, where

• a and b are the shorter sides called legs,
• and c is the longest side called the hypotenuse.

Thus, for any right triangle, the sum of the squares of the shorter sides (legs) equals the square of the longest side (the hypotenuse).

Only option C. satisfies the theorem. To show this, we can plug in 6 and 8 for a and b and 10 for c in the Pythagorean theorem and simplify:

6^2 + 8^2 = 10^2

36 + 64 = 100

100 = 100

Thus, 6, 8, 10 form a right triangle.