Question

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

Answer 1

Answer:

let them be 12x, 17x, and 25k

perimeter= sum of all sides

=> 540= 54x

=> x= 10

semi- perimeter= 540/2= 270

area=

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

=

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

= 9000 cmsq.

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

Let the side be,

• 12x
• 17x
• 25x

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

According to the question

$:\implies$ 12x +17x + 25x = 540

$:\implies$ 54x =540

$:\implies$ x = 10

Therefore the value x is 10

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

Hence,

• 12x =12 *10 =120
• 17x =17 *10=170
• 25x= 25 * 10=250

The sides of the triangle are 120,170,250

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

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.