# 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.

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> 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.      Log On

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 Question 238957: 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.Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!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.