Question

A rectangular sheet of aluminum was folded to form a rain gutter with a 31-in rectangular cross section. If the cross section has a height that is 2in. shorter than its width, how wide was the picce of aluminum before it was folded?

Answer 1

W = 6.657 in.

Step-by-step explanation

The area of a rectangle is given as

Area = L × W

Where

L = Length of the rectangle

W = Width of the rectangle

We are also told that the height (or the length) is 2 in. shorter than its width.

L = W - 2

The area of the rectangle = 31 in²

Area = L × W

31 = (W - 2) × W

W (W - 2) = 31

W² - 2W = 31

W² - 2W - 31 = 0

We now have to solve this quadratic equation. After solving,

W = 6.657 OR W = -4.657

But since the width of the rectangle cannot be negative, the right answer is

W = 6.657 in.

Hope this Helps!!!