Question

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

Answer 1

Answer:

Area of triangle= √s(s-a)(s-b)(s-c)

Here, s is the semi-permanent, and a,b,c are the sides of the triangle

Given Perimeter= 540cm

Semi-permanent = s = Perimeter/2

s = 540/2

s = 270cm

Given Ratio of sides is 12:17:25

Let sides be a = 12x

b = 17x

c = 25x

Where x is any number

Answer 2

Answer:

$\pink\bigstar$ Given

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

$\begin{gathered}\end{gathered}$

$\pink\bigstar$ To Find

• Area of Triangle

$\begin{gathered}\end{gathered}$

$\pink\bigstar$ Solution

$\underline{\pmb{\sf{\red{Let\: the\: side\: be,,}}}}$

• 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.