Answer:
Step-by-step explanation:
The area is given in two ways: 1) as a formula: A = 30w - w^2, and 2) as a specific numerical value: A = 200 m^2.
Equating these, we get:
A = 200 m^2 = A = 30w - w^2
Rewriting this equation in the standard form of a quadratic function:
-30w + w^2 + 200 m^2 = 0
or w^2 - 30w + 200 = 0, which in factored form is (w - 10)(w - 20) = 0.
Then w = 10 and w = 20.
The perimeter of the rectangle is P = 60 m, and this equals 2w + 2l. Therefore, 30 m = w + l, or l = 30 - w.
We have already found that w could be either 10 or 20.
If w = 10, then l = 30 - 10 = 20, and the perimeter would thus be:
P = 2(10) + 2(20) = 20 + 40 = 60.
This satisfies the constraints on w.
The width of the rectangle is 10 meters. The length is 20 meters.
