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

$\mathfrak{ANSWER}$

Let's take x,

⟹ Let first side be 3x

⟹ Let second side be 5x

⟹ Let third side be 7x

Given

⟹ Perimeter= 300

Therefore,,

3x + 5x + 7x = 300

8x + 7x = 300

15x = 300

x = 300/ 15

x= 20

Putting the value of x

Therefore, the value of x= 20

1st side= 3x = 3× 20 = 60

2nd side= 5x = 5× 20 = 100

3rd side = 7x = 7× 20 = 140

So, the answer is 60, 100 and 140..

Answer 2

Given :

• Sides of a triangular plot are in the ratio 3:5:7.
• Perimeter of the plot is 300m.

To Find :

• Area of the triangular plot.

Solution :

Firstly we will find the sides of triangular plot :

$\longmapsto\tt\bold{Let\:sides\:be=3x,5x\:and\:7x}$

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

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

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

$\longmapsto\tt\bold{x=20}$

So , The sides of Triangular plot are 60m , 100m and 140m.

Now ,

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

$\longmapsto\tt{\dfrac{60+100+140}{2}}$

$\longmapsto\tt{\cancel\dfrac{300}{2}}$

$\longmapsto\tt\bold{150m.}$

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

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

$\longmapsto\tt{\sqrt{150\times{(90)}\times{(50)}\times{(10)}}}$

$\longmapsto\tt{\sqrt{3\times{5}\times{5}\times{2}\times{3}\times{3}\times{5}\times{2}\times{5}\times{2}\times{5}\times{5}\times{2}}}$

$\longmapsto\tt{3\times{5}\times{5}\times{5}\times{2}\times{2}\sqrt{3}}$

$\longmapsto\tt\bold{1500\sqrt{3}{m}^{2}}$

Therefore , The Area of the Triangular Plot is 1500√3m²...