Question

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

Answer 1

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

Ratio of the sides of the triangle

= 12 : 17 : 25

★Assumption

★Ratio be p

★Sides are 12p, 17p and 25p

$\large{\fbox{Perimeter\;of\;the\;triangle= 540cm}}$

12p + 17p + 25p = 540 cm

⇒ 54p = 540 cm

${\boxed{\sf\:{p=\dfrac{540}{54}}}}$

⇒ p = 10

$\fbox{Sides\;of\;triangle\;are}$

★12p = 12 × 10

= 120 cm

★17p = 17 × 10

= 170 cm

★25p = 25 × 10

= 250 cm

$\fbox{Semi\;Perimeter :-}$

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

= 270 cm

$\large{\fbox{Using\;Herons\;Formula}}$

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

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

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

                           

 = 9000 cm²

${\boxed{\sf\:{Hence\;we\;get\;Area=9000\;cm^2}}}$

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.