Math Question #5 (2nd time asking this question)

Question

The length of a rectangle is 11 inches less than its length. The area of the rectangle is 80 square inches. Find the dimensions of the rectangle.

Answer 1

Hello, as Irene R. commented, I also believe that the width should be 11 less than the length, so I assume the question is meant to say width. The math is as follows:

What is the formula for finding the area of a rectangle? A = length x width

Width is "11 less than length." What we have here is an unknown length, x, and the width is 11 less than this x. How do we represent 11 less than? x-11

So we have set x = length, and (x-11) = width

Area = 80

A = l x w

80 = x(x-11) <--- distribute x to x and -11

80 = x² - 11x <--- subtract 80 from both sides

0 = x² - 11x - 80 <--- factor using the AC method

AC = -80, and b = -11. -16 and 5 multiply to get -80 and add up to get -11

0 = (x-16)(x+5)

Now, we must set each factor = to 0 separately.

x-16 = 0

x=16

x+5=0

x=-5

We have lengths 16 and -5. Which is correct? Length is a unit of measure, and cannot be negative. So x=-5 does not work. Thus, our length is 16 inches.

If l = 16 in, what is w? w = 16 - 11 = 5.

Dimension, 5 in x 16 in