Question

Use the Pythagorean Theorem to find x, in simplest radical form. 20

Answer 1

The Pythagorean theorem states that the sum of the squares of the two sides of a right angle is equal to the square of the hypotenuse (longest side).

`\begin{gathered} a^2+b^2=c^2 \\ \text{where }c\text{ is the hypotenuse, and }a\text{ and }b\text{ are the other two sides of a right triangle.} \end{gathered}`

Given: c = 20, a = 8, and b = x. Find x.

`\begin{gathered} a^2+b^2=c^2 \\ (8)^2+(x)^2=(20)^2 \\ 8^2+x^2=20^2^{} \\ 64+x^2=400 \\ x^2=400-64 \\ x^2=336 \\ √(x^2)=\sqrt[]{336} \\ x=\sqrt[]{16\cdot21} \\ x=4√(21)\text{ (final answer)} \end{gathered}`