Question

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

Answer 1

let the sides are 12x ,17x and 25x 

now,

perimeter =12x+17x+25x

540 = 29x+25x

540 = 54x

540/54 = x

10= x

Now,

sides are:-

12*10 = 120

17*10 =170

25*10= 250


Now,

semi- perimeter = 540/2 = 270

then,

Area by heron's formula

area = root [270(270-120)(270-170)(270-250)]

area= root [270*150*100*20]

area = root [40500 * 2000]

area = root [81,000,000]

area = 9,000


Now, 

the area of the triangle is 9000 cm^2


 i hope this will help you


-by ABHAY

Answer 2

Answer:

$\large{\underline{\underline{\bf{Given:-}}}}$

• Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm.

$\begin{gathered}\end{gathered}$

$\large{\underline{\underline{\bf{To \: Find:-}}}}$

• Area of Triangle

$\begin{gathered}\end{gathered}$

$\large{\underline{\underline{\bf{Soluntion :-}}}}$

$\underline{\pmb{\sf{\red{Let\: the\: side\: be,,}}}}$

• 12x
• 17x
• 25x

$\begin{gathered}\end{gathered}$

$\underline{\pmb{\sf{\red{According\: to\: the\: question,}}}}$

$:\implies$ 12x +17x + 25x = 540

$:\implies$ 54x =540

$:\implies$ x = 10

Therefore the value x is 10

$\begin{gathered}\end{gathered}$

$\underline{\pmb{\sf{\red{Hence,}}}}$

• 12x =12 *10 =120
• 17x =17 *10=170
• 25x= 25 * 10=250

The sides of the triangle are 120,170,250

$\begin{gathered}\end{gathered}$

$\underline{\pmb{\sf{\red{Now, To \: find\: area\: of\: triangle,}}}}$

S = a+b+c/2

$:\implies$ 120 +170 +250 /2

$:\implies$ 270

By using herons formula

$:\implies$ √s( s-a) (s-b) (s-c)

$:\implies$ √270(270-120) (2 70-170) (270-250)

$:\implies$ √270*150*100*20

$:\implies$ √81000000

$:\implies$ 9000cm

Therefore the area of the triangle is 9000 cm².