Question

The sides of a triangular plot r in the ratio of 3:5:7 and its perimeter is 300.Find its aream

Answer 1

3x + 5x + 7x=300

=15x=300

x=300/15

x=20 m

so,length of one side=60 m

length of second side=100 m

and length of third side=140 m

Now perimeter=300m

therefore semi-perimeter=150 metre

 

now according to herons formula -

 Area = root 150* (150-60) * (150-100) * (150-140)

         = root 150 * 90 * 50 * 10

         = root 30*5 * 30*3 * 5*10 *10

         = root 30^2 * 5^2 * 10^2 *3

         = 30 * 5 * 10 * root 3

         =  1500 root 3

Answer 2

Given :

• Sides of triangle in ratio 3:5:7.

To Find :

• Area of Circle

Solution :

$\longrightarrow\tt{Let\:1st\:Ratio=3x}$

$\longrightarrow\tt{Let\:2nd\:Ratio=5x}$

$\longrightarrow\tt{Let\:3rd\:Ratio=7x}$

A.T.Q :-

$\longrightarrow\tt{3x+5x+7x=300}$

$\longrightarrow\tt{15x=300}$

$\longrightarrow\tt{x=\cancel\dfrac{300}{15}}$

$\longrightarrow\tt\boxed{x=20}$

Now :

$\longrightarrow\tt{1st\:Ratio=3(20)}$

$\longrightarrow\tt\bold{60m}$

$\longrightarrow\tt{2nd\:Ratio=5(20)}$

$\longrightarrow\tt\bold{100m}$

$\longrightarrow\tt{3rd\:Ratio=7(20)}$

$\longrightarrow\tt\bold{140m}$

________________

$\longrightarrow\tt{s=\dfrac{a+b+c}{2}}$

$\longrightarrow\tt{s=\dfrac{60+100+140}{2}}$

$\longrightarrow\tt{s=\cancel\dfrac{250}{2}=150m}$

$\longrightarrow\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\longrightarrow\tt{\sqrt{150(150-60)(150-100)(150-140)}}$

$\longrightarrow\tt{\sqrt{150\times{90}\times{50}\times{10}}}$

$\longrightarrow\tt\boxed{1500\sqrt{3}{m}^{2}}$

So , The area of triangular plot is 1500√3m²...