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 1 Page 465

The value of x is 2sqrt(13), 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. 4^2+ 6^2= 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.
6^2+4^2=x^2
â–Ľ
Solve for x
36+16=x^2
52=x^2
sqrt(52)=x
x=sqrt(52)
x=sqrt(4*13)
x=sqrt(4)*sqrt(13)
x=2sqrt(13)
The value of x is 2sqrt(13).

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