The area of a playground is 221 yd^2. The width of the playground is 4 yd longer than its length. Find the length and width of the playground.

Solve w*(w-4) = 221

Width is usually less than length for a rectangle, but that is not the case here.

Try factoring
w^2 - 4w -221 = 0, and
take the positive root.

You should end up with integers for the length and the width.

w-4 is the length.

Thank you :)!

To find the length and width of the playground, we need to set up equations based on the information given. Let's use "L" to represent the length of the playground and "W" to represent the width.

We are given that the area of the playground is 221 yd^2, so we can write an equation:
L * W = 221

We are also told that the width is 4 yd longer than the length, so we can write another equation:
W = L + 4

Now we have a system of two equations with two variables. We can solve this system using substitution or elimination.

Let's use substitution. Substitute the value of W from the second equation into the first equation:
L * (L + 4) = 221

Expand the left side of the equation:
L^2 + 4L = 221

Rearrange the equation into a quadratic form:
L^2 + 4L - 221 = 0

Now we can factor or use the quadratic formula to solve for L. Since the quadratic doesn't factor easily, let's use the quadratic formula:
L = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 1, b = 4, and c = -221. Plugging in these values, we get:
L = (-4 ± √(4^2 - 4(1)(-221))) / (2(1))

Simplifying further:
L = (-4 ± √(16 + 884)) / 2
L = (-4 ± √900) / 2
L = (-4 ± 30) / 2

We have two potential solutions for L:
1. L = (-4 + 30) / 2 = 26 / 2 = 13
2. L = (-4 - 30) / 2 = -34 / 2 = -17

Since the length cannot be negative, we can discard the second solution. Therefore, the length of the playground is L = 13 yd.

Now we can substitute this value back into the second equation to find the width:
W = L + 4
W = 13 + 4
W = 17

So, the length of the playground is 13 yd, and the width is 17 yd.