Question 227978: Jenny wants to utilize a portion of her garden for growing flowers. Being a designer herself, she visualizes a triangular area with different lengths for each side. For this Jenny decides to keep a side of the triangular area 5 feet shorter than the third side and the other side 4 feet longer than the third side. She also wants to restrict the perimeter of the triangular area to a maximum of 29 feet, so that it does not cover a huge area of the garden. Determine the length of each side of the triangular area that Jenny has visualized.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let the three sides of the triangle be A, B, and C, then:
A = C-5 "One side of the triangle is 5 ft. shorter than the third side.
B = C+4 "The other side is 4 ft. longer than the third side.", and...
A+B+C = 29 ft. "...restrict the perimeter...to a maximum of 29 ft...."
Substitute the first two equations for A and B into the third equation, to get:
(C-5)+(C+4)+C = 29 Simplify.
3C-1 = 29 Add 1 to both sides.
3C = 30 Divide both sides by 3.
C = 10ft.
A = C-5
A = 5ft.
B = C+4
B = 14ft.
The sides of the triangle would be:
5ft, 14ft,and 10ft.
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