Question

A rectangle has a perimeter of 974 feet. The length is 197 feet more than the width. What is the length and width of the rectangle

Answer 1

Let's call the width of the rectangle "W" and the length "L."

From the given information, we have two pieces of information:

The perimeter of the rectangle is 974 feet. The formula for the perimeter of a rectangle is:

Perimeter = 2L + 2W

So, we can write this as:

2L + 2W = 974

The length is 197 feet more than the width. This can be expressed as:

L = W + 197

Now, we can set up a system of equations to solve for both the length and the width. We can use the second equation to express L in terms of W, and then substitute this expression into the first equation:

2(W + 197) + 2W = 974

Now, let's simplify and solve for W:

2W + 394 + 2W = 974

Combine like terms:

4W + 394 = 974

Subtract 394 from both sides:

4W = 580

Now, divide by 4 to solve for W:

W = 580 / 4

W = 145

Now that we have found the width (W), we can use the second equation to find the length (L):

L = W + 197

L = 145 + 197

L = 342

So, the width of the rectangle is 145 feet, and the length is 342 feet.

Answer 2

The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width. According to the problem, we can make the following two equations:

1) P = 2L + 2W, which is 974 = 2L + 2W

2) The length is 197 feet more than the width, which is L = W + 197

We can substitute the second equation into the first one. So, we get:

974 = 2(W + 197) + 2W
974 = 2W + 394 + 2W
974 = 4W + 394

Subtract 394 from both sides:

580 = 4W

Divide by 4:

W = 145 feet

Substitute W into the second equation:

L = 145 + 197 = 342 feet

So the length is 342 feet and the width is 145 feet.