Question

Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length l and width w. (your answer may be in terms of l and w.)

a) Area = 2lw
b) Area = 3lw
c) Area = 4lw
d) Area = lw/2

Answer 1

The maximum area of a rectangle circumscribing a given rectangle with length l and width w is (l + w) * sqrt(l^2 + w^2).

Step-by-step explanation:

To find the maximum area of a rectangle that can be circumscribed about a given rectangle with length l and width w, we need to determine the dimensions of the larger rectangle.

The larger rectangle will have a length equal to the diagonal of the given rectangle, and a width equal to the sum of the length and width of the given rectangle.

The maximum area of the larger rectangle will be equal to the product of these dimensions, which is (l + w) * sqrt(l^2 + w^2).