Solve this problem using the above process. A rectangular field is 4 times as long as it is wide. If the length is decreased by 10 feet and the width is increased by 2 feet, the perimeter will be 80 feet. Find the dimensions of the original field.

original width = 9.6 feet

original length = 38.4 feet

Step-by-step explanation:

Hi, to answer this question we have to apply the formula

P = 2w + 2 L

Where:

P=perimeter

W = width

L = length

Since the field is 4 times as long as it is wide

L = 4W

So, if the length is decreased by 10 feet and the width is increased by 2 feet, the perimeter will be 80 feet.

Mathematically speaking

80 = 2 (W+2) + 2 (L-10)

Simplifying:

80 = 2w+4 + 2L-20

Replacing the value of L by 4W

80 = 2W + 4 + 2 (4W) - 20

Solving for W:

80=2W + 4 + 8W-20

80-4+20 = 2W+8W

96 = 10W

96/10 = W

W = 9.6 feet

Replacing the value of W in the Length equation:

L = 4W

L = 4 (9.6)

L = 38.4 feet