Question

the perimeter of triangle is 540m and its sides are in ratio 12:25:17,find triangle .​

Answer 1

Correct Question :

The Perimeter of Triangle is 540m and its sides are in the ratio 12:25:17 . Find the area of Triangle.

Given :

• Sides of Triangle are in the ratio 12:25:17

To Find :

• Area of Triangle.

Solution :

• a = 12x
• b = 25x
• c = 17x

$\longmapsto\tt{12x+25x+17x=540}$

$\longmapsto\tt{54x=540}$

$\longmapsto\tt{x=\cancel\dfrac{540}{54}}$

$\longmapsto\tt\bf{x=10}$

Value of x is 10..

Therefore :

$\longmapsto\tt{First\:Side(a)=12(10)=120m}$

$\longmapsto\tt{Second\:Side(b)=25(10)=250m}$

$\longmapsto\tt{Third\:Side(c)=17(10)=170m}$

Now ,

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

$\longmapsto\tt{s=\dfrac{120+250+170}{2}}$

$\longmapsto\tt{s=\cancel\dfrac{540}{2}}$

$\longmapsto\tt\bf{s=270m}$

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

$\longmapsto\tt{\sqrt{270(270-120)(270-250)(270-170)}}$

$\longmapsto\tt{\sqrt{270(150)(20)(100)}}$

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

$\longmapsto\tt\bf{9000{m}^{2}}$

So , The Area of Triangle is 9000 m².