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.) (3 points)
pleas show me how you got the answer. Thank you:)
To find the length and width of the playground, we can set up a system of equations using the given information.
Let's assume that the length of the playground is x yards.
According to the given information, the width of the playground is 4 yards longer than its length. So, the width would be x + 4 yards.
The area of a rectangle is given by the formula: Area = length × width.
Given that the area of the playground is 221 square yards, we can set up the equation:
221 = x(x + 4)
Simplifying the equation:
221 = x^2 + 4x
Rearranging the equation to bring it to a quadratic form:
0 = x^2 + 4x - 221
Now, we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 4, and c = -221.
Plugging in the values into the quadratic formula:
x = (-4 ± sqrt(4^2 - 4(1)(-221))) / (2(1))
Simplifying further:
x = (-4 ± sqrt(16 + 884)) / 2
x = (-4 ± sqrt(900)) / 2
x = (-4 ± 30) / 2
So, we have two possible values for x:
x = (-4 + 30) / 2 or x = (-4 - 30) / 2
Solving these equations:
x = 26 / 2 or x = -34 / 2
x = 13 or x = -17
Since the length cannot be negative, we discard x = -17 as an extraneous solution.
Therefore, the length of the playground is 13 yards.
Using this information, we can find the width of the playground:
Width = Length + 4
Width = 13 + 4
Width = 17 yards
So, the length of the playground is 13 yards and the width is 17 yards.