The surface area covered by rectangular playground is 200 yards. The weight of the playground is twice as long as it’s only using factors determine the length and the width of the playground.
To determine the length and width of the playground, we need to find two factors whose product equals half of the weight of the playground.
Let x be the length and y be the width of the playground.
We know that x*y = 200. This is our first equation.
We are also told that the weight of the playground is twice as long as it is wide, so the weight equals 2y.
Half of the weight is y, so our second equation is y = y.
Now, we can substitute y = 200/x into the second equation:
y = 200/x
Substituting this expression for y into the first equation, we have:
x * (200/x) = 200
200 = 200
Simplifying, we find:
x^2 = 200
Taking the square root of both sides, we get:
x = ±√200
Since we are dealing with measurements, we cannot have negative values, so we discard x = -√200 and only consider the positive value:
x = √200
To find the other factor, we substitute this value of x into the first equation:
√200 * y = 200
y = 200 / √200
Simplifying, we have:
y = √200
Therefore, the length of the playground is approximately √200 yards and the width is approximately 200 / √200 yards.
To determine the length and width of the rectangular playground, we need to use the given information that the surface area is 200 square yards and the weight is twice as long as the width.
Let's assume the width of the playground is represented by "x" yards.
Since the surface area of a rectangle is given by the formula: Area = Length × Width, we can write:
200 = Length × Width
Substituting the given information that the weight (Length) is twice as long as the width, we have:
200 = 2x × x
Expanding the equation:
200 = 2x^2
Dividing both sides of the equation by 2:
100 = x^2
Taking the square root of both sides of the equation:
√100 = √(x^2)
10 = x
Therefore, the width of the playground is 10 yards.
Since the weight (Length) is twice the width:
Length = 2 × Width
Length = 2 × 10
Length = 20 yards
So, the length of the rectangular playground is 20 yards and the width is 10 yards.