Question

How do you determine if the lengths `36, 77, 85` form a right triangle?

Answer 1

Use the Pythagorean theorem. See the entire determination process below:

Explanation:

We will use the Pythagorean Theorem to determine if these lengths for a right triangle.

This theorem states, for a right triangle:

`a^2 + b^2 = c^2`

Where `a` and `b` are the base and height and `c` is the hypotenuse which is also the longest length.

Substitute the values into this equation and see if both sides of the equation are equal. If they are the lengths form a right triangle. If they are not equal then they would not form a right triangle.

`36^2 + 77^2 = 85^2`

`1296 + 5929 = 7225`

`7225 = 7225`

Because both sides of the equation are equal these lengths do form a right triangle.