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 8 Page 468

The value of x is 3sqrt(55), 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. 9^2+ x^2= 24^2 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+x^2=24^2
â–Ľ
Solve for x
81+x^2=576
x^2=495
x=sqrt(495)
x=sqrt(9* 55)
x=sqrt(9)*sqrt(55)
x=3sqrt(55)
The value of x is 3sqrt(55).

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