Question

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

Answer 1

Given :

⬤ Sides ot Triangle are in the Ratio 12 : 17 : 25.

⬤ Perimeter of Triangle is 540 cm.

To Find :

⬤ Area of Triangle.

Solution :

Let :

• Side A be = 12x
• Side B be = 17x
• Side C be = 25x

As given , Perimeter of Triangle is 540 cm. Hence ,

$\bf{12+17x+25x=540}$

54x = 540

x = 540/54

x = 10

Therefore , The Value of x is 10.

Hence :-

Side A = 12x

= 12(10)

= 120 cm

Side B = 17x

= 17(10)

= 170 cm

Side C = 25x

= 25(10)

= 250 cm

Now :-

s = a + b + c/2

s = 120 + 170 + 250/2

s = 540/2

s = 270

• a = 120
• b = 170
• c = 250

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

Area = √270 (270 - 120) (270 - 170) (270 - 250)

Area = √270 (150) (100) (20)

Area = √3 × 3 × 5 × 2 × 5 × 2 × 5 × 2

Area = 9000

Therefore , The Area of Triangle is 9000 cm².