Using the triangle inequality theorem, the perimeter of the triangular flower bed cannot be less than 20 meters and must be greater than 20 meters but less than 32 meters. Option C) with a 30-meter perimeter is the only feasible answer.
To find the perimeter of the triangular flower bed, we need the length of the third side, Side BC. Without the measure of an angle or additional information, we cannot calculate the exact length of the third side. However, according to the triangle inequality theorem, the length of any side of a triangle is less than the sum and more than the difference of the lengths of the other two sides. Hence, Side BC can be more than 4 meters (12m - 8m) and less than 20 meters (12m + 8m).
Options A) and B) are not possible because the perimeter must exceed the sum of the two known sides, which is 20 meters. Option C) is the only feasible answer, as it is greater than 20 meters but less than 32 meters. Therefore, the villagers can plan for the third side to be a maximum of 18 meters long (30m perimeter - 12m - 8m), adhering to the triangle inequality theorem. So, the total perimeter of the triangular flower bed is 30 meters.
The probable question may be:
In a quaint village, a triangular flower bed with only two known sides is being planned. The lengths of the known sides are as follows: Side AB is 8 meters, and Side AC is 12 meters. The villagers are excited to decorate the remaining side but are unsure of how to calculate the perimeter with just two side lengths. How can the villagers find the perimeter of this triangular flower bed with the given information, and what would be the total distance around the flower bed?
Additional Information:
Side Lengths:
Side AB: 8 meters
Side AC: 12 meters
Village Collaboration:
The village carpenter suggests exploring various options for the third side.
The florist advises considering different flower arrangements that complement the triangular shape.
Options:
A) 20 meters
B) 28 meters
C) 30 meters
D) 32 meters