The area of a playground is 35 square yards. The width of the playground is 2 yd longer than its length. Find the length and width of the playground.
Responses
L= 5 W= 7
L = 2.5 W=10
L= 10 W= 2.5
L=7 W=5
To solve this problem, we can set up an equation based on the information given. Let's represent the length of the playground as L and the width of the playground as W.
Given:
Area = 35 square yards
Width = Length + 2
We know that the formula for the area of a rectangle is Length x Width. So, we can write the equation:
35 = L x (L+2)
Expanding and simplifying:
35 = L^2 + 2L
L^2 + 2L - 35 = 0
Now, we can factor the quadratic equation:
(L + 7)(L - 5) = 0
Setting each factor to zero gives us two possible solutions:
L + 7 = 0 or L - 5 = 0
Solving for L:
L = -7 or L = 5
Since a negative length doesn't make sense in this context, we can discard L = -7.
Therefore, the length of the playground is 5 yards. Now, we can find the width using W = L + 2:
W = 5 + 2
W = 7
So, the length of the playground is 5 yards and the width is 7 yards.
Therefore, the correct answer is L = 5 W= 7.