Exercise 5 Page 468

Let's begin with recalling the Pythagorean Theorem.

In the formula, a and b are the legs and 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. 9^2+ 40^2= x^2 Let's solve above equation. Notice that, since x is a side length, we will consider only positive case when taking a square root of x^2.

9^2+40^2=x^2

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Solve for x

CalcPow

Calculate power

81+1600=x^2

AddTerms

Add terms

1681=x^2

RearrangeEqn

Rearrange equation

x^2=1681

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=sqrt(1681)

CalcRoot

Calculate root

x=41

The value of x is 41.

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