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A new Community Wellness Complex is being built in Erie. The perimeter of the rectangular playing field is 492 yards. The length of the field is 4 yards less than quadruple the width. What are the dimensions of the playing​ field?

Respuesta :

musiclover10045

Perimeter is 2 times the length plus 2 times withe width.

Let X = the width, then the length would be 4x-4

Now you have :

2(x) + 2(4x-4) = 492

Simplify:

2x + 8x - 8 = 492

Combine like terms:

10x - 8 = 492

Add 8 to both sides:

10x = 500

Divide both sides by 10:

x = 500 / 10

x = 50

The width is 50 yards.

The length = 4(50) - 4 = 200-4 = 196 yards.

The dimensions of the playing​ field will be 50 yards by 196 yards.

What is the perimeter of the rectangle?

The sum of all the sides of the rectangle will be known as the perimeter of the rectangle.

Let L be the length and W be the width of the rectangle.

Then the perimeter of the rectangle will be

Perimeter of the rectangle = 2(L + W) units

A new Community Wellness Complex is being built in Erie.

The perimeter of the rectangular playing field is 492 yards.

492 = 2 (L + W)

L + W = 246    ...1

The length of the field is 4 yards less than quadruple the width.

L = 4W - 4      ...2

From equations 1 and 2, we have

4W - 4 + W = 246

5W = 250

W = 50 yards

Then the length will be

L = 4 x 50 - 4

L = 200 - 4

L = 196 yards

The dimensions of the playing​ field will be 50 yards by 196 yards.

More about the perimeter of the rectangle link is given below.

https://brainly.com/question/15287805

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