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.

$\dfrac{40}{8}=x$

$5=x$

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.