Question

Sided of triangle are in the ratio 12 :17:25 and it perimeter is 540cm .Find i area

Answer 1

Let the common ratio be x
12:17:25 = 12x + 17x + 25x
12x + 17x + 25x = 540
54x = 540
x = 540/54
x= 10
so,
12x = 12× 10 = 120
17x= 17×10= 170
25x= 25×10=250
hence, the sides of triangle are 120cm, 170cm, 250cm
now area of triangle = =√s(s-a)(s-b)(s-c)
=√540×420×370×290
=√81000000
=9000cm^2

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