A triangle has sides of 24in, 45in, 51in. Is the triangle a right triangle?

Answer 1

To determine if the triangle is a right triangle, we can use the Pythagorean Theorem, which states that for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's label the sides of the triangle as follows:

a = 24in (one leg of the triangle)
b = 45in (one leg of the triangle)
c = 51in (hypotenuse)

Now we can calculate:

a^2 + b^2 = 24^2 + 45^2 = 576 + 2025 = 2601
c^2 = 51^2 = 2601

Since a^2 + b^2 = c^2, the triangle satisfies the Pythagorean Theorem and is a right triangle.