The length of the three sides of our triangular park is 65 meters, 70 meters and 75 meters respectively. Let us calculate the distance of the opposite vertex from the largest edge.
Answers
Answer:Given,
In a triangular park length of three sides are AB = 65 m, AC = 70 m and BC = 75 m and AD = x m, is the height of the perpendicular drawn to BC
To find,
The length of perpendicular drawn from the opposite vertex on the longest side.
Solution,
Now, the perpendicular drawn from a vertex to the opposite side, is the perpendicular height of that triangle.
By assuming the longest side as the base of the triangle, we can say that.
Area of the triangle = ½ × Base × Height
Now, we have to calculate the area of the triangle, which can be calculated by the Heron's formula.
First of all, we need to calculate the semi perimeter of the given triangle.
Semi perimeter of the given triangle = (65+70+75)/2 = 210/2 = 105 m
Area of the given triangle = ✓105× (105-65) × (105-70) × (105-75) = ✓(105×40×35×30) = ✓4410000 = 2100 m²
Now,by putting the values,
2100 = ½ × 75 × height
height = 2100 × 2 × 1/75
height = 56
Hence, the length of the given perpendicular will be 56 metres.
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