The area of a playground is 221 yd2. The width of the playground is 4 yd longer than its length. Find the length and width of the playground.
(Hint: Include correct units in your final answer.)
Area = L * W
W = L + 4
Substitute L + 4 for W in the first equation to find L. Put that value in the second equation to find W. to Check, put both values into the first equation.
To find the length and width of the playground, let's assign variables to the unknowns. Let's say the length of the playground is "x" yards.
According to the problem, the width of the playground is 4 yards longer than the length. So the width would be "x + 4" yards.
The formula for the area of a rectangle is length times width. Therefore, we can set up the following equation:
x * (x + 4) = 221
Now we can solve the equation for "x" to find the length of the playground.
x^2 + 4x = 221
x^2 + 4x - 221 = 0
Now we can use quadratic formula to solve for "x":
x = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = 1, b = 4, and c = -221.
x = (-4 ± √(4^2 - 4 * 1 * -221)) / (2 * 1)
x = (-4 ± √(16 + 884)) / 2
x = (-4 ± √900) / 2
x = (-4 ± 30) / 2
Now we have two possible solutions for "x":
1. x = (-4 + 30) / 2 = 26 / 2 = 13
2. x = (-4 - 30) / 2 = -34 / 2 = -17
Since we can't have negative length for the playground, we discard the second solution. Therefore, the length of the playground is 13 yards.
And since the width is 4 yards longer than the length, the width would be 13 + 4 = 17 yards.
So, the length of the playground is 13 yards and the width is 17 yards.