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 4 Page 468

The value of x is 34, and the side lengths 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. 16^2+ 30^2= x^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.
16^2+30^2=x^2
â–Ľ
Solve for x
256+900=x^2
1156=x^2
x^2=1156
x=sqrt(1156)
x=34
The value of x is 34.

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