Question

The length of the rectangle is fourteen more than three times the width. The perimeter of the rectangle is 204 feet. Find the dimensions of the rectangle.

Answer 1

Length l = 58ft

Width w = 22ft

Explanation:

Given;

Perimeter P = 204 ft

Length = fourteen more than three times the width

Let w represent the width of the rectangle;

Length l = 3w + 14 .....1

Perimeter of a rectangle can be written as;

P = 2l +2w

Substituting the values of l and w;

P = 2(3w+14) + 2w = 8w + 28

And P = 204 ft

8w + 28 = 204

8w = 204-28

8w = 176

w = 176/8

w = 22ft

Since;

l = 2w +14

l = 2(22) + 14

l = 58ft

Length l = 58ft

Width w = 22ft

Answer 2

Length = 80 feet, Width = 22 feet

Explanation:

Let's call the length 'L' and the width 'W'. Then, we can formulate the following equations:

L = 3*W + 14

2L + 2W = 204 -> L + W = 102

Using the value of L from the first equation in the second equation, we have that:

3*W + 14 + W = 102

4*W = 88

W = 22 feet

From the first equation:

L = 3*W + 14 = 66 + 14 = 80 feet.