Question

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Answer 1

Answer:

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

Answer 2

$\large{\sf{\red{\underline{\underline{Heya}}}}}$

Ratio between the sides of triangle = 12:17:25

Let the ratio be x

First side =12x

Second side = 17x

Third side = 25x

Perimeter = 540 cm

Perimeter of triangle = 12x+17x+25x

540= 12x+17x+25x

540 = 54x

54x=540

$\frac{540}{54}$

x= 10

First side = 12× 10

120cm

Second side = 17×10

170cm

Third side = 25×10

250cm

Area of triangle :

Using herons formulae

Semi perimeter of triangle = 540/2

Semi perimeter = 270

$\sqrt{270(270 - 120)(270 - 170)(270 - 250)}$

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

Area = ${9000}$

9000 cm square