Solve the problem.
-A rain gutter is made from sheets of aluminum that are 27 inches wide. The edges are turned up to form right angles. Determine the depth of the gutter that will allow a cross-sectional area of 54 square inches.
There are two solutions to this problem. Round to the nearest tenth of an inch.
A)2.4 in. and 11.1 in.
B)2.2 in. and 24.8 in.
C)2.9 in. and 13.3 in.
D)1.7 in. and 19.9 in.

Question

Quizplus · Accepted Answer

Let the depth of the gutter be x inches. Then the width of the base of the gutter will be 27-2x inches (since the edges are turned up to form right angles). The cross-sectional area of the gutter is the product of the width and depth, which is given to be 54 square inches. Therefore:

(27-2x)x = 54
27x - 2x^2 = 54
2x^2 - 27x + 54 = 0

Using the quadratic formula, we get:

x = (27 ± sqrt(729-432))/4
x = (27 ± 9sqrt(3))/4

The two possible solutions are:

x ≈ 2.4 inches
x ≈ 11.1 inches

Since the gutter cannot be that deep, we choose the solution that is more reasonable, which is x ≈ 2.4 inches. Therefore, the answer is A).

Solve the Problem. -A Rain Gutter Is Made from Sheets of Aluminum That