a triangular plot with sides 28 meters, 35 meters n 56 meters is to be surrounded by a fence built on pillars set 7 meters apart, after pillars are placed at each corner, how may additional pillar will be needed ?
To calculate the number of additional pillars needed for the fence, we need to determine the length of each side of the triangle that will be formed by the pillars.
The total length of the fence is the sum of the three sides of the triangular plot:
28 + 35 + 56 = 119 meters
Since the pillars are set 7 meters apart, we need to divide the total length by the distance between the pillars to find the number of intervals between the pillars:
119 / 7 = 17 intervals
However, we also need to take into account the pillars at the corners, which would be 3 additional pillars (one at each corner), located at the beginning and end of each side. Therefore, we subtract 3 from the total number of intervals:
17 - 3 = 14 additional pillars
Thus, 14 additional pillars will be needed in addition to the ones placed at each corner.
To find out how many additional pillars will be needed, we need to calculate the perimeter of the triangular plot and then divide it by the distance between each pillar.
Perimeter of the triangular plot = Sum of all sides
Perimeter = 28 meters + 35 meters + 56 meters
Perimeter = 119 meters
Now, let's find out how many pillars can be placed on the perimeter considering they are set 7 meters apart.
Number of pillars = Perimeter / Distance between each pillar
Number of pillars = 119 meters / 7 meters
Number of pillars ≈ 17
However, the triangular plot already has pillars at each corner, so we need to subtract these from the total number of pillars.
Additional pillars needed = Number of pillars - Pillars at corners
Additional pillars needed = 17 - 3
Additional pillars needed = 14
Therefore, 14 additional pillars will be needed to surround the triangular plot.
To determine the number of additional pillars needed, we need to calculate the perimeter of the triangular plot and then divide it by the spacing between each pillar.
Step 1: Calculate the perimeter of the triangular plot.
The perimeter of a triangle is the sum of its three sides.
Perimeter = Side1 + Side2 + Side3
Given:
Side1 = 28 meters
Side2 = 35 meters
Side3 = 56 meters
Perimeter = 28 + 35 + 56 = 119 meters
Step 2: Determine the spacing between each pillar.
The pillars are set 7 meters apart. Since there are no pillars on the corners yet, deductions need to be made. In the case of a triangular plot, the number of deductions is equal to the number of corners.
Number of corners = 3
Deductions = Number of corners × Spacing between pillars
Deductions = 3 × 7 = 21 meters
Effective perimeter = Perimeter - Deductions
Effective perimeter = 119 - 21 = 98 meters
Step 3: Calculate the number of additional pillars needed.
The additional pillars can be determined by dividing the effective perimeter by the spacing between each pillar.
Number of additional pillars = Effective perimeter / Spacing between pillars
Number of additional pillars = 98 / 7 = 14
Therefore, 14 additional pillars will be needed after placing the initial pillars at each corner.