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 = Β±β200
Since we are dealing with measurements, we cannot have negative values, so we discard x = -β200 and only consider the positive value:
x = β200
To find the other factor, we substitute this value of x into the first equation:
β200 * y = 200
y = 200 / β200
Simplifying, we have:
y = β200
Therefore, the length of the playground is approximately β200 yards and the width is approximately 200 / β200 yards.