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 ->  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


   

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) About Me  (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:
A+=+d%2Aw 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%2Bw+=+20 and
2) d%2Aw+=+50
Rewrite equation 1) as w+=+20-2d and substitute into equation 2).
2a) d%2820-2d%29+=+50 Simplify and solve for d, the depth.
2b) 20d-2d%5E2+=+50 Rewrite as a quadratic equation in standard form.
2c) 2d%5E2-20d%2B50+=+0 Solve by factoring.
2d) %282d-10%29%28d-5%29+=+0 Apply the zero product rule.
2e) 2d-10+=+0 or d-5+=+0 which means that...
highlight%28d+=+5%29
The depth of the gutter is 5 inches.