Exercise 7 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. 8^2+ x^2= 17^2 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.

8^2+x^2=17^2

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Solve for x

CalcPow

Calculate power

64+x^2=289

SubEqn

LHS-64=RHS-64

x^2=225

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=sqrt(225)

CalcRoot

Calculate root

x=15

The value of x is 15.

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