College Algebra

Question

        HOUSE
________________
l        l         l         l
l        l         l         l    HOUSE
l        l         l         l
l____ l_____l_____l

(the dashed lines are x)
Mary wishes to use two sides of her house to enclose a rectangular garden which is shown above. She has 72 ft of fencing at her disposal.
Find the value of x which yields the maximum area:_____ft.
Determine the maximum area:_____ft.

Answer 1

3 widths and 1 length is the Perimeter.

72 = 3X + L

L = 72 - 3x

Area = length x width
Area(x) = x ( 72 - 3x)

The max occurs at the average of the zeros.
The zeros are x=0 and 72-3x = 0
72 = 3x
x = 72/3 = 24

The average of the zeros is (0+24)/2 = 24/2 = 12

The width x = 12 ---> L = 72 - 3(12) = 72 - 36 = 36.
The max area is 12 x 36 = 432