   SEARCH HOME Math Central Quandaries & Queries  Question from Tami, a parent: The length of a rectangle is twice the width. The number of square units in it's area is four times the number of units in it's perimeter. What are the dimensions of the rectangle? Tami,

The task here is to carefully read the two sentences and turn them into equations. First you need labels for the dimensions of the rectangle, the length and the width. I am going to call them L and W.

The first sentence says "The length of a rectangle is twice the width." using my labels this is

L = 2 W

The second sentence says "The number of square units in it's area is four times the number of units in it's perimeter." The area of a rectangle is the length times the width (L W) and the perimeter is the distance all the way around so that's L + W + L + W = 2 L + 2 W. Thus the equation that comes from the second sentence is

L W = 4 (2 L + 2 W)

Substitute L = 2 into the second equation and solve for W.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.