# Simple algebra involving pythagorean theorum

#### NewSlang

##### New member
I'm trying to use an equation to determine the length of the leg of a right triangle, knowing the length of the other two sides. One leg is 90 and the hypotenuse is 150. It seems to me that the correct equation to use to solve this is:

90^2+x^2=150^2

Yet when I try to solve this equation by taking the square root of both sides, I end with "x=60" as my answer. This clearly cannot be true, and through trial and error I found the correct answer to be "x=120". Am I starting with an incorrect equation or am I solving it wrong? Either way, how do I get to the right answer by setting up an equation?

#### galactus

##### Super Moderator
Staff member
You have it set up right, just do some very minor algebra.

$$\displaystyle 90^{2}+x^{2}=150^{2}$$

$$\displaystyle x^{2}=150^{2}-90^{2}$$

$$\displaystyle x=\sqrt{150^{2}-90^{2}}$$

#### jonboy

##### Full Member
Hello, NewSlang!

NewSlang said:
Solve:$$\displaystyle \L \;90^2\,+\,x^2\,=\,150^2$$

First you always simplify the exponents:$$\displaystyle \L \;8,100\,+\,x^2\,=\,22,500$$

Isolate the $$\displaystyle x^2$$:$$\displaystyle \L \;x^2\,=\,14,400$$

.................Sqrt both sides:$$\displaystyle \L \;x\,=\,120$$

Check:$$\displaystyle \L \;90^2\,+\,(120)^2\,=\,150^2$$

.................$$\displaystyle \L \;22,500\,=\,22,500$$

#### NewSlang

##### New member
thanks that makes perfect sense now.