Question

The length of a particular rectangle is 4 greater than the width of the rectangle. If the perimeter of the rectangle is 16, what is the area of the rectangle?

Answer 1

2l+2w=perimeter <= equation for perimeter
w+4=l <=length is 4 greater than width
2w+2(w+4)=24 <= plug in the l in the first equation with the second equation
2w+2w+8=24 <= solve the equation
4w=16
w=4
and, since
w+4=l <= length is 4 greater than width
then l=4+4
l=8

Answer 2

So if we say the width is x, and the length is x+4, we know that 2(x+4) + 2x =16.

Open up the parenthesis with the distributive property, and you get 2x + 8 + 2x = 16.

Subtract 8 from both sides.

2x + 2x = 8

Or

4x = 8

/4 /4

x = 2

So therefore, since the width is x, then the width is 2. The length is x+4, or 6.

The area is length times width.

2×6 = 12

So the area of the rectangle is 12 square units.