SOLUTION: one side of a triangle is 1 ft longer then the shortest side, and the third side is as long as the shortest side. If the perimeter is less than 25 ft what is the range of the short
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Question 5075: one side of a triangle is 1 ft longer then the shortest side, and the third side is as long as the shortest side. If the perimeter is less than 25 ft what is the range of the shortest side?
A= 1/2 ab
-25= 2a -1/2b = c+ 1
It was recently brought to my attention by STAN (special thanks to Stan for reminding me about this very important "detail" concerning triangles)! This solution has now been corrected to include this additional restriction, which I have placed at the end of the solution:
"In order to be a triangle, the sum of the smaller two sides must be more than the third side.
Let x = shortest side
x+1 = second side
x = third side
Perimeter = 3x + 1 < 25
Perimeter must be > 0, so
0<3x + 1 < 25
Subtract 1 from each part:
0-1< 3x + 1 < 25 - 1
-1 < 3x < 24
Divide each part by 3:
However, x represents a side of a triangle, so x must be positive: x>0. In addition since the sum of the smaller two sides must be greater than the largest side,
