SOLUTION: 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

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Question 178241: 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 3 feet shorter and the other 2 feet longer than the third side. She also wants to restrict the perimeter of the triangular area to 32 feet, so that it does not cover a huge area of the garden. Determine the maximum length of each side of the triangular area that Jenny has visualized.
Found 2 solutions by josmiceli, nerdybill:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s= a side of the triangle
Given:
Maximum perimeter = 32 ft
One of the sides is s+-+3 ft
Another side is s+%2B+2 ft
The sum of the 3 sides is
s+%2B+s+-+3+%2B+s+%2B+2+=+3s+-+1
3s+-+1+=+32
3s+=+33
s+=+11
s+-+3+=+8
s+%2B+2+=+13
The maximum lengths of the sides is
8, 11, and 13
check:
8+%2B+11+%2B+13+=+32
32+=+32
OK

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = length of third side
then from: "3 feet shorter"
x-3 = second side
and from: "2 feet longer than the third side"
x+2 = first side
.
Because the perimeter was given as 32 feet we have:
32 = x + (x-3) + (x+2)
32 = x + x-3 + x+2
32 = 3x-1
33 = 3x
11 feet = x (third side)
.
second side:
x-3 = 11-3 = 8 feet
.
first side:
x+2 = 11+2 = 13 feet