A rectangle 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.

Length 18 units; Width 3 units

Step-by-step explanation:

Length

l = 6w

Perimeter

P = 2l + 2w = 2 (6w) + 2w = 14w = 42 - -> w = 3

l = 6*3 = 18