The perimeter of a playing field for a certain sport is 178 ft. The length is 43ft longer than the width. Find the dimensions

Question

The width of the playing field is ?? (integer or decimal)

Answer 1

The shape of the playing field would be useful here for example, if you have a rectangular playing field then you can make the proper substitutions according to the information given and set them equal to the given Perimeter

For a playing field in the shape of a rectangle

Perimeter = 2(Width) + 2(Length)

P = 2W + 2L

P = 178 ft

L = 43 ft + W

So

178 = 2W + 2(43 + W)

Distribute the 2 through the Parentheses first to give

178 = 2W + 86 + 2W

Combine like terms

178 = 4W + 86

Subtract 86 from both sides of the equation to give

92 = 4W

Divide both sides of the equation by 4 to solve for W to give

23 = W

Substitute this value in the equation for L to find the Length

L = 43 + W

L = 43 + 23

L = 66

Dimensions for a rectangular playing field are

Width = 23 ft

Length = 66 ft

Check the values against the Perimeter

178 = 2(23) + 2(66)

178 = 46 + 132

178 = 178

This is suitable for a playing field in the shape of a Rectangle. You can use the same concept for another shape.

I hope you find this useful, if you have any questions, please send me a message.