Question

The length L of a rectangle is 4 units more than its width W. The rectangle's are is 252 square units. A) Write the equation that you would use to solve this problem by completing the square relating the area to the width. B) What is the width of the rectangle? C) What is the length of the rectangle?

Answer 1

w=14

l=18

Explanation:

To find the dimensions, create an equation for its area and solve for each using the area formula A = l*w. The dimensions given are A = 252, w for width and l= w+4 (4 more than the width).

`A = l*w\\252 = (w+4)*w\\252 = w^2+4w\\252+4 = w^2 +4w +4\\256 = (w+2)^2\\√(256) =√((w+2)^2) \\16 = w+2\\16 = w+2\\14= w\\`

The width is 14 so the length is l=w+4 or l= (14)+4 =18