The length of a new rectangular playing field is 8 yards longer than triple the width. If the perimeter is 464 yards what are its dimensions

Answer 1

Hello Jason,

In order to determine the field's dimensions, we will need to first establish two expressions to represent the length and width of the field. Since it is a rectangle, we then need to use the perimeter to calculate the real values of the length and width.

So, first let the following be true:

Let x equal the width:

Let 3x + 8 equal the length:

Second, the formula for calculating the perimeter of a rectangle is as follows:

P = 2 (L + W) or P = 2(L) + 2(W) due to the distributive law or property of mathematics. P equals the perimeter - which is given in your problem - L equals the length and W equals the width in both formulas. I prefer using the second formula, so let's start with that, okay?

P = 2(L) + 2(W)

464 = 2(3x + 8) + 2(x)

464 = 6x + 16 +2x

464 = 8x + 16

448 = 8x

x = 56 <------This is the width, okay?

To determine the length, all we need do is substitute 56 for the value of "x." You will recall that the length is 3x + 8. Therefore:

3x + 8 =

3(56) + 8 =

168 + 8 =

3x + 8 = 176 <-----This is the length, okay?

Finally, we should always check our work, right? Therefore, all we need do is to use the formula for perimeter with the other side's information ensuring it equals the given perimeter of the field which is 464 yards.

P = 2 (L + W)

464 = 2(176 + 56)

464 = 2(232)

464 = 464

The answer checks so therefore, the dimensions of the rectangular playing field, given the information in your problem is:

176 yards by 56 yards with the length being 176 yards and width being 56 yards.

I hope this helps you and that you have a great week. Best!