other one math problem?

Question

a kennel owner has 164 feet of fencing with which to enclose a rectangular region. He wants to subdivide this region into three smaller rectangles of equal length. If the total area to be enclosed is 576 square feet, find the dimension of the entire enclosed region. (hint: write an expression for l in terms of w)

Answer 1

1/2(164-4w)w=576
-2w^2 +82w-576=0
2w^2-82w+576=0
w^2 -41w +288=0
(w-32)(w-9)=-0
w = 32 or 9
the dimension = 32 x 18 or 9x64

Answer 2

Given:
164 feet = perimeter of the rectangular region to be fenced
576 sq.ft = total area to be enclosed

Find:
a) L = length of the rectangular region
b) W = width of the rectangular region

Solution:
Perimeter of Rectangle, P = 2L + 2W
Area of Rectangle, A = LW
576 ft^2 = LW
L = 576 ft^2/W. Substitute this into the perimeter equation:

P = 2L + 2W
164 ft = 2(576 fr^2/W) + 2W
164 = 1152/W + 2W
W(164) = 1152 + 2W^2
164W = 1152 + 2W^2
2W^2 - 164W + 1152 = 0
W^2 - 82W + 576 = 0

W = {-(-82) +/- sqrt[(-82)^2 - 4(1)(576)]}/2(1)
W = 7.76 ft or 74.24

When W = 7.76 ft, L = 576/7.76 = 74.24 ft
When W = 74.24 ft, L = 576/74.24 = 7.76 ft

The most logical way of dividing the rectangular region into three smaller rectangles is to draw two horizontal line segments parallel to either of the width. Hence, the width of the each smaller rectangle is 74.24ft/3 = 24.75 ft. Hence the
dimension of each smaller rectangle is 24.75 ft by 7.76 ft.

ANSWERS: 24.75 ft by 7.76 ft

teddy boy

Answer 3

576 sq. f.t divided by 3= 192 sq. ft. for each rectangle