Question:
A farmer plants trees in a triangular arrangement where the length of one side of the triangle is 4x+64x + 64x+6 meters, the second side is 3x+23x + 23x+2 meters, and the third side is 2x+42x + 42x+4 meters. What is the expression for the semi-perimeter of the triangle?
Options: A) 4.5x+64.5x + 64.5x+6 meters
B) 4.5x+84.5x + 84.5x+8 meters
C) 4.5x+94.5x + 94.5x+9 meters
D) 5.5x+65.5x + 65.5x+6 meters
Solution
The semi-perimeter sss is half of the perimeter. First, find the perimeter by adding the sides:Perimeter=(4x+6)+(3x+2)+(2x+4)=9x+12\text{Perimeter} = (4x + 6) + (3x + 2) + (2x + 4) = 9x + 12Perimeter=(4x+6)+(3x+2)+(2x+4)=9x+12
The semi-perimeter is half of the perimeter:Semi-perimeter=9x+122=4.5x+6\text{Semi-perimeter} = \frac{9x + 12}{2} = 4.5x + 6Semi-perimeter=29x+12=4.5x+6
So, the correct answer is A) 4.5x+64.5x + 64.5x+6 meters.
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