Question

A rectangle with an area of 240 in2 has a length 10 inches shorter than five times its width. Which equation could be used to solve for the length of the rectangle?

Answer 1

L = 5W - 10
5W = L + 10
W = 1/5(L + 10)
Area = L x W
240 = L(1/5(L + 10)
L^2 + 10L = 240(5) = 1200
L^2 + 10L - 1,200 = 0

Answer 2

The equation which can be used to solve for the length of the rectangle : x² - 2x - 48 = 0

Explanation:

Let width of the rectangle be x inches

Now, The rectangle has length 10 inches shorter than five times its width

⇒ Length of rectangle = 5x - 10

Now, Area of rectangle is given to be : Area = 240 inches²

Also, Area of the rectangle is given by the formula : Area = Length × Width

⇒ 240 = (5x - 10) × x

⇒ 5x² -10x = 240

⇒ 5x² - 10x - 240 = 0

⇒ x² - 2x - 48 = 0

Therefore, The equation which can be used to solve for the length of the rectangle : x² - 2x - 48 = 0