Question

Find the dimensions of a rectangle with perimeter 108 m whose area is as large as possible. (If both values are the same number, enter it into both blanks.)smaller value

Answer 1

Explanation:

rectangle perimeter = 2×length + 2×width = 108 m

length + width = 54 m

length = 54 - width

rectangle area A = length×width = max.

A(width) = (54 - width) × width = -width² + 54×width

we get the extreme points of a function by finding the zeroes of the 1st derivative.

A'(width) = -2×width + 54 = 0

2×width = 54

width = 27 m

so, the max. area is achieved with a width of 27 m.

length = 54 - width = 54 - 27 = 27 m.