Question

A piece of sheet metal, w = 20 inches wide, is bent to form the guttershown in the illustration. If the cross-sectional area is 18 square inches,find the depth of the gutter.Tho Yilar County News earns a profit of $20 per year for each of its 3,000

Answer 1

The width of the sheet is 20 inches:

$w=20$

The cross-sectional area is 18 square inches.

From the diagram provided, the cross-sectional area is calculated to be:

$A=(w-2x)(x)$

Therefore, we have that:

$(w-2x)(x)=18$

Expanding the equation, we have:

$wx-2x^2=18$

If we substitute the value of w into the equation, we have:

$20x-2x^2=18$

We can divide through by 2 and rearrange the equation. Thus, we have:

$x^2-10x+9=0$

Solving the quadratic equation by factorization, we have:

$\begin{gathered} x^2-9x-x+9=0 \\ x(x-9)-1(x-9)=0 \\ (x-9)(x-1)=0 \\ \therefore \\ x=9\text{ or 1} \end{gathered}$

Therefore, the depth of the gutter can be 1 inch or 9 inches.