SOLUTION: A garden in the shape of a right triangle has sides measuring 60, 80 and 100 ft. The owner of the garden adds a new section of fence that runs from the right angle to the hypotene

Question 126833: A garden in the shape of a right triangle has sides measuring 60, 80 and 100 ft. The owner of the garden adds a new section of fence that runs from the right angle to the hypoteneuse and separates the garden into two parts of equal perimeter. Find the length of the new section of the fence. Problem is not out of a textbook, rather on a worksheet.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A garden in the shape of a right triangle has sides measuring 60, 80 and 100 ft. The owner of the garden adds a new section of fence that runs from the right angle to the hypotenuse and separates the garden into two parts of equal perimeter. Find the length of the new section of the fence.
:
Draw the triangle ABC, (B=90) with a=60, b=100; c=80
Let D = point on side b where the new section of fence BD will be joined
:
The perimeters are give as equal so we can say:
CD + 60 + BD = AD + 80 + BD
Subtract BD from both sides
CD + 60 = AD + 80
:
We know that CD + AD = 100
CD = (100-AD)
:
Substitute (100-AD for CD; find AD
100 - AD + 60 = AD + 80
160 = AD + AD + 80
160 - 80 = 2AD
AD =
AD = 40,
then
100-40 = 60 is CD
:
We have to find the length of BD which is the new fence
Cos C = .6
:
Using triangle BCD, find BD, (c in the formula)
Using the law of cosines:
c^2 = a^2 + b^2 - 2(ab)*Cos C
BD^2 = 60^2 + 60^2 - 2(60*60) * .6
BD^2 = 3600 + 3600 - 2(3600) *.6
BD^2 = 7200 .6(7200)
BD^2 = 7200 - 4320
BD = SqRT(2880)
BD = 53.6656, say 54 ft of additional fencing required

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