Exercise 2 Page 465

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. 3^2+ x^2= 5^2 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.

3^2+x^2=5^2

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Solve for x

CalcPow

Calculate power

9+x^2=25

SubEqn

LHS-9=RHS-9

x^2=16

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=sqrt(4)

CalcRoot

Calculate root

x=4

The value of x is 4.

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