Question

A triangle has sides 35cm, 54cm and 61cm long.find its area. Also find the smallest of its altitude

Answer 1

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Answer 2

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here's ur answer...

given the sides of the triangle are 35cm, 54cm and 61cm.

semi perimeter of the triangle = ( 35 + 54 + 61 )/2

= 150/2

= 75cm

let the sides of the triangle be a, b and c.


$area \: of \: the \: triangle \: by \: herons \: \\ formula = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{75(75 - 35)(75 - 54)(75 - 61)} \\ \\ = \sqrt{75 \times 40 \times 21 \times 14} \\ \\ = \sqrt{882000} \\ \\ = 420 \sqrt{5} \: {cm}^{2} \\ \\ = 939.14 {cm}^{2} (approx)$

the smallest side of this triangle is 35cm.

let it be the base.

therefore 1/2 × b × h = 939.14cm²

==> 1/2 × 35 × h = 939.14cm²

==> 17.5 × h = 939.14cm²

==> h = 939.14/17.5

==> h = 53.66cm (approx)

hence the altitude of the triangle by taking the smallest side as base is 53.66cm.

hope this helps..!!