Question 238957
Let d = the depth of the gutter and w = its width.
The area of the cross-section can be expressed as:
{{{A = d*w}}} and this is given as 50 sq.in.
The cross-section however consists of only three sides, d+d+w and the sum of these dimensions is given as 20 in.
So we can write the following:
1) {{{2d+w = 20}}} and
2) {{{d*w = 50}}} 
Rewrite equation 1) as {{{w = 20-2d}}} and substitute into equation 2).
2a) {{{d(20-2d) = 50}}} Simplify and solve for d, the depth.
2b) {{{20d-2d^2 = 50}}} Rewrite as a quadratic equation in standard form.
2c) {{{2d^2-20d+50 = 0}}} Solve by factoring.
2d) {{{(2d-10)(d-5) = 0}}} Apply the zero product rule.
2e) {{{2d-10 = 0}}} or {{{d-5 = 0}}} which means that...
{{{highlight(d = 5)}}}
The depth of the gutter is 5 inches.