Question

The length of a rectangle is six times its width. If the perimeter of the rectangle is 140 yd, find its length and width.

Answer 1

`\boxed{ \sf{length \: of \: a \: rectangle = 60 \: yd}}`

`\boxed{ \sf{width \: of \: a \: rectangle = 10 \: yd}}`

Explanation:

Let the width of a rectangle be 'w'

Length of a rectangle ( l ) = 6w

Perimeter of a rectangle ( P ) = 140 yd

Finding the width of a rectangle

`\boxed{ \sf{perimeter \: of \: rectangle= 2(length + breadth)}}`

`\dashrightarrow{ \sf{140 = 2(6w + w)}}`

`\dashrightarrow{ \sf{140 = 2 * 7w}}`

`\dashrightarrow{ \sf{140 = 14w}}`

`\dashrightarrow{ \sf{14w = 140}}`

`\dashrightarrow{ \sf{ (14w)/(14) = (140)/(14)}}`

`\dashrightarrow{ \sf{w = 10}}`

Width of a rectangle = 10 yd

Now, replacing / substituting the value of w in 6w in order to find the length of a rectangle

`\dashrightarrow{ \sf{length = 6 * x = 6 * 10 = 60 \: yd}}`

Length of a rectangle = 60 yd

Hope I helped!

Best regards! :D