Question

A triangle shaped land has the sides
in the ratio 3:5:7, if its perimeter is
300 meter. What will be the area of
the land ? ​

Answer 1

HELLO DEAR,

GIVEN:-

sides of triangle are in ratio of 3 : 5 : 7.

perimeter of triangle is p = 300m

NOW,

let the sides of triangle be 3x , 5x , 7x.

therefore,

p = 3x + 5x + 7x

=> 300 = 8x + 7x

=> 300 = 15x

=> x = 20m.

hence, side of triangle be 3x , 5x , 7x

or 60 , 100 , 140 respectively.

since, area of triangle = $\sf{\sqrt{s(s - a)*(s - b)*(s - c)}}$

where a , b , c are the sides of triangle and s is the semiperimeter of triangle.

s = p/2 = 150m

$\sf{ \rightarrow A = \sqrt{150(150 - 60)(150 - 100)(150 - 140)}}$

$\sf{\rightarrow A = \sqrt{150*90*50*10}}$

$\sf{\rightarrow A = 100\sqrt{15*15*3}}$

$\sf{\rightarrow A = 1500\sqrt{3}meters}$

I HOPE IT'S HELP YOU DEAR,

THANKS