Question

The length of a picture is 15.75 inches shorter than twice the width. If the perimeter of the picture is 106.5 inches, find its dimensions

Answer 1

Length = 45.37 in

Width = 30.56 in

Explanation:

Let the width of the picture be 'w' inches.

Given:

Perimeter of the picture is,
`P=106.5\ in`

Length is 15.75 inches shorter than twice the width. So, length is:

`l=2w-15.75`

Now, we know that the perimeter of a rectangular shape is given as the sum of all of its side. So, the picture is also of rectangular shape and hence the perimeter is given as:

`P=2l+2w`

Plug in the values of 'l' and 'P' and solve for 'w'. This gives,

`106.5=2w-15.75+2w\\106.5=4w-15.75\\106.5+15.75=4w\\4w=122.25\\w=(122.25)/(4)=30.56\ in`

Therefore, the width of the rectangular picture is 30.56 inches.

Length of the picture is,
`l=2(30.56)-15.75=61.12-15.75=45.37\ in`

So, length of the picture is 45.37 inches and width is 30.56 inches.