Question

The perimeter of a rectangle is 96 ft. How do you find the dimensions of the rectangle if the ratio of the length to the width is 7: 5?

Answer 1

The dimensions are:

length `=color(blue)( 28 feet`
the width`= color(blue)( 20 feet`

Explanation:

The ratio of dimensions (length :width) is `color(blue)(7:5`

Let us denote the dimensions as:
length (l) `=color(blue)(7x`

width (w)`=color(blue)(5x`

The perimeter of the rectangle is calculated as :
Perimeter `= 2 xx (l+ w)`

`= 2 xx ( 7x +5x)`

`= 2 xx ( 12x )`

`= 24x`

As per data provided the perimeter `=96 feet`

So, `24x = 96`
`x = 4 feet`

So:
the length `= 7x = 7 xx 4 =color(blue)( 28 feet`
the width`= 5x = 5 xx 4 =color(blue)( 20 feet`