Answer:
Step-by-step explanation:
<u>Method 1: Pythagorean Theorem</u>
We can use the Pythagorean Theorem to solve for . The Pythagorean Theorem states that in a right triangle, the sum of the squares of the legs' side lengths is equal to the length of the hypotenuse squared. Simply put, , where and are the legs and is the hypotenuse. In this case, we know that , , and , so we get:
(Substitute , , and into )
(Simplify exponents)
(Subtract from both sides of the equation to isolate )
(Simplify)
(Take the square root of both sides)
(Simplify, remember that each positive number has two square roots: a positive one and a negative one)
In the context of the situation, we know that is an extraneous solution because a polygon cannot have negative side lengths. Therefore, the final answer is .
<u>Method 2: Pythagorean Triples</u>
Method 1 works, but there's an easier way to find the value of . If we look at the given lengths of and , we can observe that this triangle is a right triangle enlarged by a scale factor of , because and . The only side length that's missing is the . Therefore, . Hope this helps!