# Find the Side length of the shaded isosceles triangle

Picture of the Problem

How would one go about solving this problem? The question is asking you to find the length of X in the picture. The only thing they give us is the area of the shaded region, which is 3003cm^2. I've tried finding multiple solutions to this problem and can't find anything. Any help would be greatly appreciated.

The area is the summation of the area of triangle and rectangle which is: $$\frac{x^2}{2}+x=3003\to x=\sqrt{6007}-1$$
• The area of triangle is $\frac{x^2}{2}$ and that of rectangle is $x$. Both are with unit Cm^2. then we have $\frac{x^2}{2}+x=3003$ or $x^2+2x=6006$ or $x^2+2x+1=6007$ which leads to $(x+1)^2=6007$ and $x=\sqrt 6007-1$ – Mostafa Ayaz Jan 19 '18 at 2:35
I think it is a trapezium and the larger base is $x$. The area of the trapezium is: $$S=\frac{x+1}{2}\cdot x=3003 \Rightarrow x=77.$$