Question

Solve each problem by applying the four steps of problem solving. Use the strategy of solving an algebraic equation for each problem. A rectangular field is 5 times longer than it is wide. If the perimeter is 540 feet, what are the dimensions (length and width) of the field?

Short answer

Question: Find the length and width of a rectangular field whose length is 5 times the width and has a perimeter of 540 feet. Answer: The dimensions of the rectangular field are 225 feet in length and 45 feet in width.

Step-by-step solution

Define variables and equations

Let L represent the length and W represent the width. We are given that the length is 5 times the width, so L = 5W. We are also told that the perimeter is 540 feet, so we use the formula for the perimeter of a rectangle: P = 2L + 2W. Now we have the following system: - L = 5W - P = 2L + 2W where P = 540

Substitute L in the perimeter equation

Replace L with 5W in the perimeter equation: 540 = 2(5W) + 2W

Solve for W

Solve for W in the equation: 540 = 10W + 2W 540 = 12W W = \dfrac{540}{12} W = 45

Solve for L

Now that we have found the width (W=45), we can use L = 5W to determine the length: L = 5(45) L = 225 So, the dimensions of the rectangular field are length (L) = 225 feet and width (W) = 45 feet.