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: 30.25 inches

Width: 23 inches

Explanation:

Let

x ---> the length of the picture in inches

y ---> the width of the picture in inches

we know that

The perimeter of the picture is equal to

`P=2(x+y)`

we have

`P=106.5\ in`

so

`106.5=2(x+y)`

simplify

`53.25=x+y` ----> equation A

`x=2y-15.75` ----> equation B

Solve the system by substitution

substitute equation B in equation A

`53.25=(2y-15.75)+y`

solve for y

`53.25+15.75=2y+y`

`3y=69`

`y=23\ in`

Find the value of x

`x=2(23)-15.75=30.25\ in`

therefore

The dimensions of the picture are

Length: 30.25 inches

Width: 23 inches