Question

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

Answer 1

Answer:

9000 cm^2

Step-by-step explanation:

let side 1 = 12a

let side 2 = 17a

let side 3 = 25a

Perimeter = 540cm

side 1 + side 2 + side 3 = perimeter

12a + 17a + 25a = 540

54a = 540

a = 540\54 = 10cm

side 1 = 120cm

side 2 = 170cm

side 3 = 250cm

s = a\2 + b\2 + c\2

= 120\2 + 170\2 + 250\2

= 540\2 = 270\2

area = √270 (270 - 120) (270 - 170) (270 - 250)

= √270 (150) (100) (20)

= √81000000

= 9000cm^2

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.