Question

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

Answer 1

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.

Answer 2

Length 18 units ; Width 3 units

Explanation:

Length

l = 6w

Perimeter

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

l = 6*3 = 18