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=10^2

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Solve for x

CalcPow

Calculate power

36+x^2=100

SubEqn

LHS-36=RHS-36

x^2=64

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=sqrt(64)

CalcRoot

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.