Arectangle has a length six times the width. if the perimeter is 42 units find the width and length

Let “x” be the width. Then the length would be 6x (6 times the width “x”). We know the perimeter is the sum of all the sides of a shape, and since a rectangle has two pairs of equal sides (x and x; 6x and 6x) then all we need to do is add all the sides and isolate x.

P = 2 width + 2 length
42 = 2*x + 2*6x
42 = 2x + 12x
42 = 14x
x = 42/14
x = 3

So the width is 3 units and the length is 6*3 units, or 18 units.