Question

(50 pts will mark brainliest) The perimeter of a rectangle is 48 inches. The width of the rectangle is 4 inches more than 3 times the length of the rectangle. What are the dimensions of the rectangle?

Answer 1

Answer:

The rectangle is 5 inches long by 19 inches wide.

Step-by-step explanation:

Let's start by listing what we know:

• The perimeter of a rectangle is 48 inches.
• The width of the rectangle is 4 inches more than 3 times the length of the rectangle.

Let's represent the width with "w" and length with "l", and make a system of equations based on what we know.

$\left \{ {{2w + 2l = 48} \atop {w = 3l + 4}} \right.$

Now, let's solve the system of equations using substitution:

$2w + 2l = 48$

$2 (3l + 4) + 2l = 48$

$6l + 8 + 2l = 48$

$8l + 8 = 48$

$8l = 40$

$l = 5$

The length of the rectangle is 5 inches.

Now, let's use this to solve for the width.

$w = 3l + 4$

$w = 3(5) + 4$

$w = 15 + 4$

$w = 19$

The width of the rectangle is 19 inches.

Let's check our work:

$2w + 2l = 48$

$2(19) + 2(5) = 48$

$38 + 10 = 48$

$48 = 48$

The results match, so our answer is correct.

The rectangle is 5 inches long by 19 inches wide.