SOLUTION: An open rectangular gutter is made by turning up the sides of a piece of metal 20in. wide. The area of the cross-section of the gutter is 50in^2. Find the depth of the gutter.

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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:
1) and
2)
Rewrite equation 1) as and substitute into equation 2).
2a) Simplify and solve for d, the depth.
2b) Rewrite as a quadratic equation in standard form.
2c) Solve by factoring.
2d) Apply the zero product rule.
2e) or which means that...

The depth of the gutter is 5 inches.