Question

The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m . Find its area ​

Answer 1

Answer:

1500 square root 3 m^2

Step-by-step explanation:

The sides of a the triangular plot are in the ratio 3:5:73:5:7. So, let the sides of the triangle be 3x3x, 5x5x and 7x7x.

Also it is given that the perimeter of the triangle is 300300 m therefore,

3x+5x+7x=3003x+5x+7x=300

15x=30015x=300

x=20x=20

Therefore, the sides of the triangle are 60,10060,100 and 140140.

Now using herons formula:

S=60+100+1402=3002=150S=60+100+1402=3002=150 m

Area of the triangle is:

A=√s(s−a)(s−b)(s−c)=√150(150−60)(150−100)(150−140)=√150×90×50×10=√6750000A=s(s−a)(s−b)(s−c)=150(150−60)(150−100)(150−140)=150×90×50×10=6750000

=1500√3=15003 m22

Hence, area of the triangular plot is 1500√315003 m22.

I hope is this answer will help full.