Question

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

Answer 1

Step-by-step explanation:

ratio 12:17:25

let ratio be multiple of x

12x:17x:25x

perimeter 540 cm

12x+17x+25x=540

54x=540

x=540\54

x=10

12^10=120

17^10=170

25^10=250

s=a+b+c\2

120+170+540\2

540\2

270

now u can solve it using herons formula

mark me as brainlist

and

follow me

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

Sides be 12p , 17p and 25p

$\textbf{\underline{Hence}}$

12p + 17p + 25p = 540

29p + 25p = 540

54p = 540

$\tt{\rightarrow p=\dfrac{540}{54}}$

p = 10

Now,

$\textbf{\underline{Sides\;are:-}}$

12p = 12 × 10 = 120 cm

17p = 17 × 10 = 170 cm

25p = 25 × 10 = 250 cm

$\textbf{\underline{Hence}}$

${\boxed{\sf\:{s=\dfrac{120+170+250}{2}}}}$

$\tt{\rightarrow s=\dfrac{540}{2}}$

s = 270 cm

${\boxed{\sf\:{Using\;Heron\;Formula}}}$

$\tt{\rightarrow\sqrt{s(s-a)(s-b)(s-c)}}$

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

$\tt{\rightarrow\sqrt{270\times 150\times 100\times 20}}$

= 9000 cm²