A rectangle has a length six times the width. If the perimeter is 42 units find the width and length

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

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.