Question

Solve for x. Leave your answer in simplest radical form.

Answer 1

`x=√(31)`

Explanation:

We can use the Pythagorean theorem to evaluate x.

The formula for the Pythagorean theorem is

`a^2+b^2=c^2`

Lets look at the bottom triangle.

We are given both legs of the triangle. We can evaluate the hypotenuse.

`3^2+3^2=c^2\\9+9=c^2\\18=c^2\\√(18) =c\\3√(2) =c`

Lets look at the top triangle.

Notice the hypotenuse in the bottom triangle is the same length as one of the legs in the triangle on the top.

We are given 1 leg and the hypotenuse. We can evaluate the missing leg.

`x^2+(3√(2))^2=7^2\\x^2+3^2√(2) ^2=7^2\\x^2+9√(2) ^2=7^2\\x^2*+9*2=7^2\\x^2+18=7^2\\x^2+18=49\\x^2=49-18\\x^2=31\\x=√(31)`