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To find the value of X in this example, notice that we have a right triangle so we can use the** Pythagorean theorem.**

The Pythagorean theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the

square of the length of the hypotenuse (or **a** squared plus **b** squared equals **c **squared, where **a** and **b** are the lengths of

the legs of the right triangle and **c** is the length of the hypotenuse).

So here, since the legs of the right triangle have lengths **6** and **8** and the hypotenuse has a length of **x** we can set up the

equation 6 squared plus 8 squared equals x squared. Simplifying from here 6 squared is 6 times 6 or 36 and 8 squared

is 8 times 8 or 64, so we have 36 plus 64 equals x squared. Next 36 plus 64 is 100 and we have 100 equals x squared.

Now, to get x by itself, since x is squared we take** the square root of both sides** of the equation.

On the right the square root of x squared is x and on the left, since 100 is the perfect square 10 times 10, the square

root of 100 is 10.

So 10 equals x.

Notice that we don't use plus or minus 10 because x represents the length of the hypotenuse of the triangle which cannot

be negative.

So the value of x is 10.

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