Lindsey N. answered • 03/22/16

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Hello Heidi, this is a great question.

To solve problems like these, you need to translate the words into equations.

"The room has an area of 176 square feet." means

Area = 176

Area of a rectangle is also length times width which gives:

l * w = 176

"and is 5 feet longer than it is wide" means

length = width + 5

l = w + 5

Now that we have both equations we can use substitution to get that the area is:

w * (w + 5) = 176

Even though you've tagged this problem as completing the square, I think it makes more sense to solve it using factoring techniques. Distributing the w gives:

w

^{2}+ 5w = 176Rearranging to get the equation in standard form gives:

w

^{2}+ 5w - 176 = 0Now, 176 does not factor extremely easily. There are a lot of different factoring techniques you can use. When I divide 176 by 2, I see that 2 and 88 are factors. So I have that 2*8*11= 176 or 16*11=176. This pair meets the requirements of the problem where the room is 11 feet wide and 16 feet long. Looking at it mathematically:

(w + 16)(w - 11) = 0

The positive root of this equation is w = 11. Returning to the equation that length = width + 5 gives that length = 11 + 5, which returns 16 feet.