Question

find the area of the triangle whose sides are 13cm,20cm and 21cm Also find the altitude of the triangle corresponding to the largest side

Answer 1

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Answer 2

As given,

=> a = 13 cm
=> b = 20 cm
=> c = 21 cm

Now, We have to find Semi- Perimeter

=> S = a+b+c/2
=> S = 13+20+21/2
=> S = 54/2
=> S = 27

Now, Area of triangle,

$= > area \: = \sqrt{s(s - a)(s - b)(s - c)}$

$= > area = \sqrt{27(27 - 13)(27 - 20)(27 - 21)}$

$= > area = \sqrt{27 \times 14 \times 7 \times 6}$

$= > area = \sqrt{3 \times 3 \times 3 \times 7 \times 2 \times 7 \times 2 \times 3}$

$= > area = 3 \times 3 \times 7 \times 2$
$= > area = 126 \: {cm}^{2}$

Now, We are required to find out Altitude :-

Here, longest side will 21 cm

Area of Triangle = 1/2 x b x h

=> 126 cm^2 = 1/2 x 20 x h

=> 126 cm^2 = 10 h

=> (126/10) cm = h

=> 12.6 cm = h

=> h = 12.6 cm

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