a rectangle has a length of 18 ft less than 7 times its width. If the area of the rectangle is 405 square feet, find the length of the rectangle.

Question

This is a geometry question that i am stuck on trying to find the width of the rectangle.

Answer 1

Hi Meghan H.

w = 9 ft

l = 45 ft

For a Rectangle, Area = lw

Given

Area = 405 ft²

l = 7w - 18

w = w

We can just plug these in

405 = w(7w - 18)

405 = 7w² - 18w

We can move everything over to one side of the equal sign to yield a quadratic by subtracting 405 from both sides

0 = 7w² - 18w - 405

This can be factored

(7w + 45)(w - 9)

w = 9 since the width cannot be negative

w = 9 ft

l = 7w - 18 = 7(9) - 18 = 63 - 18 = 45

l = 45 ft

I hope this helps