Question

The length of a rectangle is 3 inches less than three times its width. The perimeter of the rectangle is 34 inches. Find the dimensions of the rectangle

Answer 1

Given:

The length of a rectangle is 3 inches less than three times its width.

The perimeter of the rectangle is 34 inches.

To find:

The dimensions of the rectangle.

Solution:

Let x be the width of the rectangle. Then, the length of a rectangle is 3 inches less than three times its width.

Length of the rectangle = 3x-3

Now, perimeter of the rectangle is

`Perimeter=2(Length + Width)`

`Perimeter=2(3x-3+x)`

The perimeter of the rectangle is 34 inches.

`34=2(4x-3)`

`34=8x-6`

`34+6=8x`

`40=8x`

Divide both sides by 8.

`(40)/(8)=x`

`5=x`

The value of x is 5. So, width of the rectangle is 5 inches.

`Length=3x-3`

`Length=3(5)-3`

`Length=15-3`

`Length=12`

Therefore, the length of the rectangle is 12 inches and the width of the rectangle is 5 inches.