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:

⇒Let x be common ratio

∴ Sides of triangle will be: 12x,17x and 25x

⇒Perimeter =540 cm(given)

⇒12x+17x+25x=540 cm,

⇒54x=540 cm

⇒x=10 cm

∴ Sides of triangle: a=120,b=170,c=250 cms

⇒2S=540

⇒S=270 cm

A=

s(s−a)(s−b)(s−c)

=

270(270−120)(270−170)(270−250)

cm

2

=

270×150×100×20

cm

2

A=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.