Question

A triangle has sides with lengths of 40 inches, 75 inches, and 85 inches. Is it a right triangle?

Answer 1

Answer: yes

Explanation:

To test if this is a right triangle, let's test these side lengths with the Pythagorean Theorem.

a^2 + b^2 = c^2

c is the hypotenuse, the longest side of a right triangle.

a and b are the legs of the right triangle.

40²+75²=85²

1600+5625=7225

7225=722

Answer 2

To determine whether the given triangle is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) 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:

side a = 40 inches

side b = 75 inches

side c = 85 inches (the longest side)

Now we can apply the Pythagorean theorem:

c^2 = a^2 + b^2

85^2 = 40^2 + 75^2

7225 = 1600 + 5625

7225 = 7225

Since the equation is true, we can conclude that the given triangle is a right triangle.