If 61 is the longest side length in the triangle , find the value of x that makes the triangle above a right triangle.

A right triangle is a triangle that has a 90° degree side. The hypotenuse is the largest side while the legs are the other two sides. To solve this problem we must use the Pythagorean Theorem as follows:

By using the quadratic formula:

Since lengths only admit positive number, we only have one solution which is:

5 is the value for x.

Step-by-step explanation:

By Pythagorean Theorem we have:

Expand the binomial square using :

Combine like terms:

Subtract 61 on both sides:

Divide both sides by 2:

Find two numbers that multiply to be -30 and add to be 1.

Those numbers are 6 and -5 so the factored form is:

This implies:

or

Solving the first equation by subtracting 6 on both sides gives:

Solving the second equation by adding 5 on both sides gives:

So since a side measurement can bot be negative units long, the only answer that x can be is 5.

Let's check:

true

step-by-step explanation: