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Let d = the depth of the gutter and w = its width.
The area of the cross-section can be expressed as:
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:
Rewrite equation 1) as
and substitute into equation 2).
Simplify and solve for d, the depth.
Rewrite as a quadratic equation in standard form.
Solve by factoring.
Apply the zero product rule.
which means that...
The depth of the gutter is 5 inches.