Question

A triangle has sides 35cm,54cm and 61cm long.Find it's area,also find the smallest of it's altitudes​

Answer 1

hiii!!!

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.

\begin{lgathered}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)\end{lgathered}areaofthetrianglebyheronsformula=s(s−a)(s−b)(s−c)=75(75−35)(75−54)(75−61)=75×40×21×14=882000=4205cm2=939.14cm2(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..!!

Answer 2

Step-by-step explanation:

A triangle has sides 35 cm 54 cm and 61 cm.

Let a = 35 cm, b = 54 cm and c = 61 cm

s = (a + b + c)/2 = 75 cm

Using Heron's formula

Area of triangle we get 420√5 cm2

Using Area of triangle = 1/2 × bh = 420√5 cm2

1/2 × 35 × h = 420√5

h = 24√5 cm

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