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?

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

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.