Find the area of a triangle whose sides are 34 CM 20 cm and 42 CM has to find the length of the altitude corresponding to the shortest side
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Semiperimeter (s) = (42 + 34 + 20 ) / 2
So it is = 96 / 2 = 48 cm.
Using herons formula = (√s )(√s-a )(√s-b) (√s-c)
By substituting s and a , b , c i.e the given sides.
We have √48 × √6 × √14 × √28
So √ (4 × 6 × 2) × √6 × √(7 × 2) × √(7 × 4)
Simplifying the numbers we have area = 4 × 6 × 2 × 7 = 336 cm ²
Hence area is 336 cm²
Now height corresponding to longest side implies that base is 42 cm and area remains same
So area of triangle is 1/ 2 b × h
336 = 1/ 2 × 42 × H
HENCE H = 16 cm
So height is 16 cm .
So it is = 96 / 2 = 48 cm.
Using herons formula = (√s )(√s-a )(√s-b) (√s-c)
By substituting s and a , b , c i.e the given sides.
We have √48 × √6 × √14 × √28
So √ (4 × 6 × 2) × √6 × √(7 × 2) × √(7 × 4)
Simplifying the numbers we have area = 4 × 6 × 2 × 7 = 336 cm ²
Hence area is 336 cm²
Now height corresponding to longest side implies that base is 42 cm and area remains same
So area of triangle is 1/ 2 b × h
336 = 1/ 2 × 42 × H
HENCE H = 16 cm
So height is 16 cm .
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