Question

The sides of a triangle are in the ratio 12: 17: 25 and its perimeter is 540cm. The area is:
a. 1000 sq.cm.
b. 5000 sq.cm.
c. 9000 sq.cm.
d. 8000 sq.cm.
tell me full ans

Answer 1

Let the sides of the triangle be 12x, 17x and 25x

Perimeter of the triangle = 540 cm

∴ 12x + 17x + 25x = 540

⇒ 54x = 540 ⇒ x = 10

Let a = 12x = 12 x 10 = 120 cm

b = 17x = 17 x 10 = 170 cm

c = 25x = 25 x 10 = 250 cm

s = (a + b + c)/2 = (120 + 170 + 250)/2 = 540/2

= 270 cm

∴ Area of triangle = root under (√s(s -a) (s -b)(s -c))

= root under (√270(270 - 120)(270 - 170)(270 - 250))

= root under (√270 x 150 x 100 x 20)

= 100 under root(√27 x 15 x 20)

= 100 x 9 x 5 x 2

= 9000 cm2

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Answer 2

Let the sides of the triangle be 12x, 17x and 25x

Perimeter of the triangle = 540 cm  

∴   12x + 17x + 25x = 540    

⇒  54x = 540    ⇒   x = 10

Let  a = 12x = 12 x 10 = 120 cm

b = 17x = 17 x 10 = 170 cm  

c = 25x = 25 x 10 = 250 cm

s = (a + b + c)/2 =  (120 + 170 + 250)/2 = 540/2

= 270 cm

∴   Area of triangle  =  root under (√s(s -a) (s -b)(s -c))

=  root under (√270(270 - 120)(270 - 170)(270 - 250))  

=   root under (√270 x 150 x 100 x 20)  

= 100 under root(√27 x 15 x 20)

= 100 x 9 x 5 x 2  

= 9000 cm2