Question

The rectangle shown has a perimeter of 54 cm and the given area. Its length is 3 more than twice its width. Write and solve a system of equations to find the dimensions of the rectangle. The length of the rectangle is _ cm and the width of the rectangle is _ cm.

Answer 1

length of the rectangle is 19 cm and the width of the rectangle is 8 cm.

Explanation:

The formula for the perimeter of a rectangle = 2L + 2 W

Where:

L = length and W = width

The rectangle shown has a perimeter of 54 cm

Its length is 3 more than twice its width.

2L + 2W = 54 .... Equation 1

"length is 3 more than twice its width."

L = 2W + 3.....Equation 2

Substituting 2W + 3 for L

We have:

2L + 2W = 54 .... Equation 1

2(2W + 3) + 2W = 54

4W + 6 + 2W = 54

6W = 54 - 6

6W = 48

W = 48/6

W = 8cm

L = 2W + 3.....Equation 2

L = 2(8) + 3

L = 16 + 3

L = 19 cm

Therefore:

length of the rectangle is 19 cm and the width of the rectangle is 8 cm.