The width and length

Question

A community Sports complex is being built in Madison. The perimeter of the rectangular playing field is 458 yards. The length of the field is 6 yards less than quadruple the width. What are the dimensions of the playing field?

The width is ___ yards.

The length is ___ yards.

Answer 1

Perimeter = 2(L+W) = 458 => L+W =229

L = 4W - 6

Substitute :

4W - 6 + W = 229

5W=235

You solve it from here.

Answer 2

The key to this question is being able to successfully write an equation that illustrates the relationship between the two sides.

We are given this relationship: "The length of the field is 6 yards less than quadruple the width." Let's translate this statement piece by piece.

Starting from the back, we have "quadruple the width." If we let W=width, you could write this algebraically as 4W. "6 yards less than" can be written as minus 6; and "The length of the field is" can be written as L =, if we let L stand for length.

Putting all that together as the sentence is written, we come up with L = 4W - 6

The perimeter of a rectangle is found using the following formula: P = 2W + 2L. Knowing that the perimeter is 458, we can say that 458 = 2W + 2L

We can now use a system of equations to solve this problem. Since the first equation is already solved for L, it will be most efficient to use the substitution method. If we substitute L (from the first equation) into the second equation, we get

458 = 2W + 2(4W - 6).

Distributing the 2 gives

458 = 2W + 8W - 12

Adding the 12 to both sides gives

470 = 2W + 8W

Collecting like terms gives

470 = 10W

Dividing both sides by 10 gives

47 = W.

Now that we have solved for the width, we plug in our width value to either of our original equations to get the value of the length. Plugging the value of the width into the first equation gives

L = 4(47) - 6

Multiplying 4 and 47 gives

L = 188 - 6

Taking 6 from 188 gives

L = 182

Therefore:

The width is 47 yards

The length is 182 yards

Answer 3

458 = 2(4w - 6 + w)

229 = 5w - 6

5w = 235

w = 47 yds

l = 4(47) - 6

l = 188 - 6

l = 182 yds