The area A, in square meters, of a rectangle with a perimeter of 60 meters is given by the equation A = 30w - w2, where w is the width of the rectangle in meters. What is the width of a rectangle if its area is 200 m2? m

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.