Notice that one side of the playground does not require fencing.
1250ft^2
Practice makes perfect
Let's define a variable for each dimension of the rectangle. Let w be the width and l be the length.
The perimeter of a rectangle is P=2l + 2w, but one side does not require fencing. This means the perimeter of the playground is P=2l + w. Since there is 100ft of fence, then 2l+w = 100, which means that w = 100 - 2l.
Now, we can write the area of the rectangular playground.
A=l* w ⇔ A = l(100-2l)
This is a quadratic function that models the area of the playground. Let's rewrite it in standard form.
ccc
A(l) = l(100-2l) ⇕ A(l) = -2l^2 + 100l + 0
Let's identify the coefficients of the above quadratic function. As we can see a = - 2, b = 100, and c = 0.
Since a is a negative number the parabola opens downward, which implies that its maximum point corresponds to the vertex. Let's find the x-coordinate of the vertex.
l = -b/2 a ⇔ l = -100/2( -2)
Let's simplify above quotient to calculate l.
