The area of a playground is 108 yd2. The width of the playground is 3 yards longer than its length. Find the length and width of the playground.
(1 point)
a. length = 12 yd, width = 9 yd
b. length = 9 yd, width = 12 yd
c. length = 12 yd, width = 15 yd
d. length = 15 yd, width = 12 yd
Let's denote the length of the playground as L and the width as W.
According to the problem, we have the following information:
1) The area of the playground is 108 yd^2, so we have the equation:
L * W = 108
2) The width of the playground is 3 yards longer than its length, so we have the equation:
W = L + 3
To solve this system of equations, we can substitute the value of W from equation 2) into equation 1):
L * (L + 3) = 108
Now we have a quadratic equation:
L^2 + 3L - 108 = 0
To solve this equation, we can factor it or use the quadratic formula. Let's factor it:
(L + 12)(L - 9) = 0
From this, we can see that L = -12 or L = 9. Since length can't be negative, we have L = 9.
Now we can substitute this value back into equation 2) to find the value of W:
W = L + 3 = 9 + 3 = 12
So the length of the playground is 9 yd and the width is 12 yd.
Therefore, the correct answer is option b. length = 9 yd, width = 12 yd.