Question

the sides of a triangle are in the ratio of 12:17:25 and it's perimeter is 540 cm find its area

Answer 1

Let length of first side of triangle =a=12x cm

 

Let length of second side of triangle =b=17x cm

 

Let length of third side of triangle =c=25x cm

 

Perimeter of triangle =540 cm

 

 

So, we get 12x+17x+25x=540

=>54x=540

=>x=540/54=>10

So, length of first side of triangle =a=12x=12×10=120 cm

 

Length of second side of triangle =b=17x=17×10=170 cm

 
Length of third side of triangle =c=25x=25×10=250 cm

 

 

Semi-perimeter of triangle =s=a+b+c/2=120+170+250/2=270 cm


Using Heron's formula to find area of triangle, we get

 

Area of triangle =s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√=270(270−120)(270−170)(270−250)−−−−−−−−−−−−−−−−−−−−−−−−√

 

√270×150×100×20=9000 cm*2



I hope it will help you.......

Answer 2

Sides are 12x ,17x,25x.
Perimeter=sum of all sides
540=17x+12x+25x.
540=54x.
x=10
12x=12×10=120
17x=17×10=170
25x=25×10=250

By heron formula,
S=a+b+c/2=120+170+250/2
540/2=270.

√S(s-a)(s-b)(s-c)=√270(270-120)(270-170)(270-250).
√270×150×100×20.