Question 978300: Mr. Bonifacio wouldlike to enclose his two adjacent rectangular gardens with 70.5 m of fencing materials. The gardens are of the same size and their total area is 180 m2
1. How would you represent the dimensions of each garden?
2. What mathematical sentence would represent the length of fencing materials to be used in enclosing the two gardens?
3. How will you find the dimensions of each gardens?
4. What equations will you use in finding the dimensuons of each garden?
5. How would you describe the equations formulated in item 4? How are you going to find the solutions of this equations?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Mr. Bonifacio would like to enclose his two adjacent rectangular gardens with 70.5 m of fencing materials.
The gardens are of the same size and their total area is 180 m2
:
Like this two long sides, three widths:
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:
2L + 3W = 70.5
divide equation by 2
L + 1.5W = 35.25
L = 35.25 - 1.5W
:
L * W = 180
replace L with (35.25-1.5W)
(35.25 - 1.5W) * W = 180
35.25W - 1.5W^2 = 180
A quadratic equation
-1.5W^2 + 35.25W - 180 = 0
Using the quadratic formula, I got two solutions
W = 16.0; not reasonable for the width
and
W = 7.5 meters is the width
:
Find the length using the area
L = 180/7.5 = 24 meters is the length
:
:
See if that checks out
2(24) + 3(7.5} =
48 + 22.5 = 70.5 meters of fencing in required
:
You should be able to answer those questions now.
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