A rectangle with positive area has a length that is three less than the width x Write an equation in terms of x that represents the length

Question

Write an equation in terms of x for the area of the rectangle. Using your answer to partb write and and solve an equation to find the length and the width of the rectangle if the area is 54 square inches.

Answer 1

Hello Kacie,

The formula for the area of a rectangle is length (y) times width (x). This rectangle's length is 3 less than the width, so y = x - 3 (that's the eqn for length in terms of x). We also know that the area is 54, so xy = 54.

Substituting for y, get x(x-3) = 54 -> x² - 3x = 54 -> x² - 3x - 54 = 0. Now have to factor: (x - 9)(x + 6) = 0.

So x must be 9, because it can't be neg. 6. If x is 9, y is 54/9 = 6, or 9 - 3 = 6 using the other eqn. Length is 6, width is 9. (Last time I checked, length was usually longer than width, but maybe this one is sitting on its short side!)