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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.

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The area is the summation of the area of triangle and rectangle which is: $$\frac{x^2}{2}+x=3003\to x=\sqrt{6007}-1$$

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  • $\begingroup$ If you don't mind me asking, where does that -1 come from? I know that the model shows the 1cm, but how does that play into the problem? $\endgroup$ – Killiyana Jan 19 '18 at 2:29
  • $\begingroup$ 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 $x=\sqrt 6007-1$ $\endgroup$ – Mostafa Ayaz Jan 19 '18 at 2:35
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I think it is a trapezium and the larger base is $x$. The area of the trapezium is: $$S=\frac{x+1}{2}\cdot x=3003 \Rightarrow x=77.$$

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