Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
1. The Pythagorean Theorem
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Exercise 10 Page 468

The value of x is 4sqrt(2), and the side lengths do not form a Pythagorean triple.

Practice makes perfect

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. x^2+ 7^2= 9^2 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.
x^2+7^2=9^2
â–Ľ
Solve for x
x^2+49=81
x^2=32
x=sqrt(32)
x=sqrt(16* 2)
x=sqrt(16)*sqrt(2)
x=4sqrt(2)
The value of x is 4sqrt(2).

Notice that not all side lengths of the triangle are integers, so they do not form a Pythagorean triple.