A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, find the height of the parallelpgram.
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Given : If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm,
Let the length of the sides of the triangle are a = 13 cm, b = 14 cm and c = 15 cm.
Let s be the semi perimeter of the triangle.
s = (a + b + c)/2
s = (13 + 14 + 15)/2
s = 42/2
s = 21 cm
Using heron’s formula,
Area of the triangle, A = √s (s - a) (s - b) (s - c)
A = √21(21 – 13) (21 – 14) (21 – 15)
A = √21 × 8 × 7 × 6
A = √(7 × 3) × (4 × 2) × (7) × (3 × 2)
A = √(7 × 7) × (3 × 3) × (2 × 2) × (4)
A = 7 × 3 × 2 × 2
A = 21 × 4
Area of the triangle = 84 m²
Let height of parallelogram be h & Base = 14 (given)
It is given that Area of parallelogram = Area of triangle :
Area of parallelogram = base × height
84 = 14 × h
h = 84/14 cm
h = 6 cm
Hence, the height of the parallelogram is 6 cm.
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