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:

Let the sides be 3a, 5a and 7a.

Perimeter = sum of all sides

= > 3a + 5a + 7a = 300

= > 15a = 300

= > a = 300/15

= > a = 20 m

Sides are -

3a = 3(20m) = 60m

5a = 5(20m) = 100m

7a = 7(20m) = 140m

Semi - perimeter = 300/2 = 150

Using heron's formula-

= > $\sqrt{150*(150-60)(150-100)(150-140)}$

= > $\sqrt{150*90*50*10}$

= > $\sqrt{15*9*5*10^4}$

= > $\sqrt{3*5*9*5*10^4}$

= > $5*3*10^2 \sqrt3$

= > 1500$\sqrt3$

Area is 1500 $\sqrt3$ m^2

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...