a playground is 5 meters longer than its width. what are the dimension of itd area ia 968m. squared
solve for x
x(x+5) = 968
(hint you should get x = appr 28.7 )
To find the dimensions of the playground, we can set up equations based on the given information:
Let's say the width of the playground is "x" meters.
According to the given information, the playground is 5 meters longer than its width. So, the length would be "x + 5" meters.
The formula for the area of a rectangle is length multiplied by width:
Area = Length * Width
Given that the area is 968 square meters, we can write the equation:
968 = (x + 5) * x
To solve this equation, we can simplify it and bring it to the standard quadratic form:
968 = x^2 + 5x
Rearranging the equation:
x^2 + 5x - 968 = 0
Now, we can solve this quadratic equation to find the values of "x" using factoring, completing the square, or the quadratic formula.
Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
For our equation:
a = 1, b = 5, c = -968
Plugging in these values into the quadratic formula, we get:
x = (-5 ± √(5^2 - 4*1*(-968))) / (2*1)
Simplifying further:
x = (-5 ± √(25 + 3872)) / 2
x = (-5 ± √(3897)) / 2
Since we are dealing with measurements, we will only consider the positive value of "x" (width cannot be negative):
x = (-5 + √(3897)) / 2 ≈ 30.73
Now we have the width of the playground, x ≈ 30.73 meters.
To find the length, we can substitute this value back into the expression for the length:
Length = x + 5 ≈ 30.73 + 5 ≈ 35.73 meters
So, the dimensions of the playground are approximately 30.73 meters for the width and 35.73 meters for the length.