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 :

Given sides of Triangle are in ratio = 3:5:7

So, Let the sides of the Triangle be 3x,5x,7x

Now, Given Perimeter = 300 m

As we know that

Perimeter of Triangle = Sum of its sides

Therefore, 300 = 3x + 5x + 7x

=> 300 = 15x
or, 15x = 300

=> x = 300÷15

=> x = 20

Hence, Sides of Triangle are :

3(20) = 60m
5(20) = 100m
7(20) = 140m

Let side = 60m be a
=> side = 100m be b
=> side = 140m be c

Now Area of Triangle -----

$\sqrt{s(s - a)(s - b)(s - c)} \\ \\ semi \: perimeter \: = \frac{perimeter}{2} \\ \\ s = \: \frac{300}{2} \\ \\ s \: = 150 \: m \\ \\ = > \: \sqrt{150(150 - 60)(150 - 100)(150 - 140)} \\ \\ = > \: \sqrt{150 \times 90 \times 50 \times 10} \\ \\ = > \: \sqrt{6750000} \\ \\ = > \: 1500 \sqrt{3}$

Therefore Area of Triangle is 1500√3 m^2

Hope it would help you