Exercise 41 Page 500

Let's begin by recalling the Pythagorean Theorem.

In the formula, $a$ and $b$ are the legs while $c$ is the hypotenuse of a right triangle. Now let's take a look at the given triangle.

To find

x,

we will write the equation according to the Pythagorean Theorem.

6^{2} + x^{2} = 10^{2}

Let's solve above equation. Since

x

is a side length, we will only consider the positive value when taking the square root of

x^{2} .

6^{2} + x^{2} = 1 0^{2}

▼

Solve for

x

Calculate power

36 + x^{2} = 100

$LHS - 36 = RHS - 36$

x^{2} = 64

$LHS = RHS$

x = 64

Calculate root

x = 8

The value of

x

is

8 .

Notice that all side lengths of the triangle are integers, so they form a Pythagorean triple.