Question

the mean deviation about mean of the digits 1,2,3,4,5,6,7,8,9​

Answer 1

SolutioN :-

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Let the sides of triangle be 13x , 14x and 15x

Then , the perimeter of triangle = 13x + 14x + 15x

But , it is given that perimeter = 84

So , 13x + 14x + 15x = 84

$\small{ \sf \: \implies \: 42x = 84}$

$\small{ \sf \: \implies \:x = \frac{84}{42} }$

$\small{ \sf \: \implies \:x = 2 }$

$\boxed{ \mathrm{x = 2}}$

Let the first side be a , second side b and third side be c of a triangle.

Then , by putting the value of x

• a = 13x = 13 × 2 = 26
• b = 14x = 14 × 2 = 28
• c = 15x = 15 × 2 = 30

Now ,

By using Heron's formula , we have

$\boxed{\sf \small \: area = \sqrt{s(s - a)(s - b)(s - c)} }$

Where ,

• $\sf {s = \frac{perimeter}{2} }$
• a, b, c are the three sides of triangle.

By putting their values ,

$\small\sf{area \: of \: \triangle = \sqrt{ \frac{84}{2}( \frac{84}{2} - 26)( \frac{84}{2} - 28) ( \frac{84}{2} - 30 )} }$

$\small \sf{ \implies \: area \: of \: \triangle = \sqrt{42(42 - 26)(42 - 28)(42 - 30)} }$

$\small \sf{ \implies \: area \:of \: \triangle = \sqrt{42(16)(14)(12)} }$

$\small \sf{ \implies \: area \: of \: \triangle = \sqrt{42 \times 16 \times 14 \times 12} }$

$\small \sf{ \implies \: area \: of \: \triangle = \sqrt{112896} }$

$\small \sf{ \implies \: area \: of \: \triangle = {336 \: cm}^{2} }$

Therefore, area of triangle = 336m²