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If the altitudes of a triangle are in the ratio 2:3:4, then the lenghts of corresponding sides are in the ratio: please give the solution.

If the altitudes of a triangle are in the ratio 2:3:4, then the lenghts of corresponding sides are in the ratio:
please give the solution.

Grade:11

1 Answers

Sunil Raikwar
askIITians Faculty 45 Points
7 years ago
let the altitudes be 2x, 3x, 4x & the corresponding sides be a,b,c.
we know that area of triangle=1/2{ base* corresponding height}
so
1/2(2x*a)=1/2(3x*b)=1/2(4x*c)=area of triangle(let k)
2a=3b=4c=k
a=k/2, b=k/3, c=k/4
a:b:c=1/2:1/3:1/4=6:4:3

Thanks & Regards
Sunil Raikwar
askIITians faculty

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