Exercise 43 Page 500

Let's begin with 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. 27^2+ 36^2= x^2 Let's solve above equation. Since x is a side length, we will consider only positive case when taking a square root of x^2.

27^2+36^2=x^2

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Solve for x

CalcPow

Calculate power

729+1296=x^2

AddTerms

Add terms

2025=x^2

RearrangeEqn

Rearrange equation

x^2=2025

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=sqrt(2025)

CalcRoot

Calculate root

x=45

The value of x is 45.

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