Solve by factoring

Question

Find the dimensions of a rectangle whose width is 9 miles less than it's length and whose area is 70 square miles

Answer 1

We need to find the dimensions by factoring

Area of Rectangle A, is equal to the Length times the Width or L x W

A = L x W

The information given is

A = 70; W = L - 9; and L = L

70 = L(L - 9)

70 = L² - 9L

We can apply a quadratic by subtracting 70 from both sides setting the equation to 0

0 = L² - 9L - 70

We'll factor 70 to give us a difference of 9, this is where the factoring comes in

(L - 14)(L + 5) = 0

L = 14, L cannot be negative 5

To check, just plug this value back into our original substitution to get the dimensions of the rectangle

W = L - 9; 14 - 9 = 5

W = 5 miles

L = 14 miles

A = L x W

70 = 14 x 5

I hope you find this useful, if you have any questions please send me a message.