Question

In a triangle ABC, side AB measures 5 inches, side BC measures 7 inches, and side AC measures 8 inches. Is triangle ABC a right triangle?

a) Yes
b) No
c) Not enough information to determine
d) It's an obtuse triangle

Answer 1

No, triangle ABC is not a right triangle.

Step-by-step explanation:

In a triangle ABC, side AB measures 5 inches, side BC measures 7 inches, and side AC measures 8 inches. To determine if triangle ABC is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's see if the lengths of the sides of triangle ABC satisfy this condition:

AB2 + BC2 = 52 + 72 = 25 + 49 = 74

AC2 = 82 = 64

Since AB2 + BC2 is not equal to AC2, triangle ABC is not a right triangle (option b).