How to find equation for task (Image)

Question

How to find the width of x?

I tried $(x-30)(x-40)=325$ and then writing it in the form $ax^2-bx+c$ and then set it equal to zero to find the roots(?.. where y=0) using the quadratic formula.

Answer 1

HINT: we get $$(40-x)(30-x)+325=30\cdot 40$$

Answer 2

The area of the shaded portion is given by ,

$40\cdot 30 - (40-x)\cdot(30-x) = 325$

$1200-325 = (40-x)(30-x)$

$1200-70x +x^2 = 875$

$ x^2-70x +325 = 0$

Do you think you can solve for $x$ now?

Answer 3

The shaded area A is composed of the vertical and horizontal parts. The horizontal part has area $40x$, and the vertical part has area $30x$. But there's an overlapping part with area $x^2$, and thus $$ 40x + 30x - x^2 = 70x - x^2 = 325 \Rightarrow x^2 - 70x + 325 = 0 $$ Solving this equation with the quadratic formula gives us $$ x = \frac{70 \pm \sqrt{70^2-4\times 1 \times 325 }}{2} = \frac{70 \pm 60}{2} $$ and since $x<30$, we conclude $x=5$.