A triangle and parallelogram have the same base and the same area. If the sides of the triangle are 34 cm, 42 cm and 20 cm, then the height of parallelogram having base 42 cm, is equal to
Answers
Given : A triangle and parallelogram have the same base and the same area.
The sides of the triangle are 34 cm, 42 cm and 20 cm,
To Find : the height of parallelogram having base 42 cm
Solution:
The sides of the triangle are 34 cm, 42 cm and 20 cm,
s = ( 34 + 42 + 20)/2 = 48
Area = √(48)(48 - 34)(48 - 42) (48 - 20)
=> Area = √48 * 14 * 6 * 28
=> Area = √2 * 4 * 6 *2 * 7 * 6 * 4 * 7
=> area = 2 * 4 * 6 * 7
=> Area = 42 * 8
Area of parallelogram = Base * height
Hence height of the parallelogram = 8 cm
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Solution :-
Semi - perimeter of given ∆ = s = sum of all sides / 2 = 34 + 42 + 20 / 2 = 48 cm
now,
→ Area of ∆ = √[s * (s - a) * (s - b) * (s - c)]
→ Area of ∆ = √[48 * (48 - 34) * (48 - 20) * (48 - 42)]
→ Area of ∆ = √[48 * 14 * 28 * 6]
→ Area of ∆ = √[6 * 8 * 2 * 7 * 4 * 7 * 6]
→ Area of ∆ = 6 * 7 * 8
→ Area of ∆ = 336 cm² .
now, let us assume that the height of parallelogram is equal to h cm .
then,
→ Area of ll gm = 336 cm²
→ Base * height = 336
→ 42 * h = 336
→ h = 8 cm (Ans.)
Hence, the height of parallelogram is equal to 8 cm .
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