Find the dimensions of the rectangle meeting the specified conditions.

The perimeter is 352 feet and the length is 4 1/2 times the width.

width ft

length ft

1574.0

To find the dimensions of the rectangle, we need to set up an equation based on the given information.

Let's assume that the width of the rectangle is represented by the variable 'w'.

According to the given information, the length of the rectangle is 4 1/2 times the width. In other words, we can write the equation:

length = 4 1/2 * width

To simplify the equation, we need to convert the mixed number into an improper fraction.

4 1/2 = 9/2

So, the equation becomes:

length = 9/2 * width

Now, we can use the equation for the perimeter of a rectangle to solve for the dimensions.

Perimeter of a rectangle = 2(length + width)

We are given that the perimeter is 352 feet. So, we can write the equation:

352 = 2(length + width)

Substituting the value of length from the previous equation, we get:

352 = 2((9/2) * width + width)

To simplify the equation, we can multiply 2 with the terms inside the parentheses:

352 = (18/2 + 2/2) * width

Simplifying further:

352 = (20/2) * width

352 = 10 * width

Now, divide both sides of the equation by 10 to solve for the width:

width = 352 / 10

width = 35.2 feet

So, the width of the rectangle is 35.2 feet.

To find the length, we can substitute the width value back into the equation:

length = (9/2) * width

length = (9/2) * 35.2

length = 158.4 feet

So, the length of the rectangle is 158.4 feet.

Therefore, the dimensions of the rectangle are:
Width = 35.2 feet
Length = 158.4 feet