The question is as follows:

The three sides of a triangle are 10m, 15m, and 20m. What is the area of the triangle?

My diagram:

Attachment 19805
(20 - x)^2 - x^2 = 15^2 - 10^2

**Using Pythagoras' theorem**

h^2=15^2-(20-x)^2=10^2-x^2

225-(400-40x+x^2)=100-x^2

-175+40x=100
(20 -x)(20 - x) - x^2 = 125

400 - 40x -2x^2 = 125 ......

**you should have 400-40x+x^2-x^2 here**
-40x - 2x^2 = -275

x - 2x^2 = 6.875

-2x^2 = 6.875x

x^2 = -3.4375x

x = -3.4375

Obviously it's not the right answer, but I have no idea how to get the right one. Answers are greatly appreciated!