Question

The sides of a triangle are in the ratio 12: 17: 25 and its perimeter is 540cm.Find the area.

Answer 1

the sides => 12x+17x+25x= 540
=> 54x = 540. => x = 540/54. => 10 therefore sides are=>120cm,170cm and 250cm
and semi perimeter => 540/2 => 270cm
therefore area =>
$\sqrt{270(270 - 120)(270 - 170)(270250)}$
$\sqrt{270 \times 150 \times 100 \times 20}$
$= > 10 \times 10 \times 2 \times 5 \times 3 \times 3$
$= > 9000cm3$

Answer 2

let it be 12x,17x and 25x
perimeter of rectangle = a+ b+c
 540cm=12x+17x+ 25x
540cm=54x
x=540/54
     =10
lets substitiue 12x,17x and 25x
12x=120[multiplying x as 10]
17x=170[multiplying x as 10]
25x=250[multiplying x as 10]

the sides are 120 ,170 and 250
it's semipetimeter = 540/2= 270
using heron's formula area of the triangle =
root {(s)(s-a)(s-b)(s-c)}where s is the semipetimeter and a,b,c
area the sides of the triangle.
root {( 270)(270-120)(270-170)(270-250)}
= 9000cm^2.