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

Answer:

Length = 45.37 in

Width = 30.56 in

Step-by-step 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,

$106.5=2w-15.75+2w\\106.5=4w-15.75\\106.5+15.75=4w\\4w=122.25\\w=\frac{122.25}{4}=30.56\ in$

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.