Question

Kelly is gluing rectangular cards in her scrapbook. Each card has an area of 24 square inches and the length is 2 inches more than the width. If x represents the width of each card, select all of the equations that could be used to find the length and width of her cards.

Answer 1

The equation would be (w+2)(w)=24, the width would be 4 and the length would be 6.

We find the area of a rectangle by multiplying its length and width:

A = lw

The length is 2 more than the width, or l = w+2:
A = (w+2)(w)
24 = (w+2)(w)

Multiplying this through, we have:
24 = w² + 2w

We want the equation set equal to 0 to solve it, so subtract 24 from both sides:
24 - 24 = w² + 2w - 24
0 = w² + 2w - 24

This is easily factorable, as 6(-4) = -24 and 6 + -4= -2:
0 = (w+6)(w-4)

Using the zero product property, we know either w+6=0 or w-4= 0, so w=-6 or w=4. A negative width makes no sense, so w = 4. This means l = w+2 = 4+2 = 6.