Question

Find the length of a rectangle, given that the perimeter is 180 feet and the length is 5 times the width.

Answer 1

• Length of rectangle = 75 feet

Explanation:

Let us consider the width of the rectangle be 'x' feet and length be '5x' feet .

Also the perimeter of the rectangle is 180 feet

`{\boxed{\sf{Perimeter = 2(l +w)}}}`

where, l is length and w is width

`\hookrightarrow \sf 2(5x + x ) = 180`

`\hookrightarrow \sf 10x + 2x = 180`

`\hookrightarrow \sf 12x = 180`

Divide both sides by 12,

`\hookrightarrow \sf x = 15`

Hence, width of rectangle = x = 15 feet

`\hookrightarrow \sf Length = 5x`

`\hookrightarrow \sf Length = 5(15)`

`\hookrightarrow \sf Length = 75 \: feet`

Henceforth, the length of the rectangle is 75 feet.