Question

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

Answer 1

Odd number is an interview which is not a multiple of a divisible of two. If it is divided by two, the result is a fraction. One is the first odd positive number. The next four bigger numbers are 3,5,7.....

Answer 2

Given : The side of the triangle is = 12 : 17 : 25 and its perimeter is 540 cm

To find : It's area

Solution: let the common ratio be x

⟹ 12x : 17x: 25x

We know that the perimeter of the triangle =sum of the side of the triangle

⟹ perimeter of the triangle = 540 cm ( given )

Therefore,

12x + 17x + 25x = 540 cm

⟹ 54x = 540 cm

$\implies x = \dfrac{ \cancel{540}} { \cancel{54} }$

⟹ x = 10 cm

Therefore,

The sides of the triangle are

$12x = 12 \times x = 120 \: cm \\ 17x = 17 \times x = 170 \: cm\\ 25x = 25 \times x = 250 \: cm$

Now,

The semiperimeter of the triangle =

$\dfrac{ \cancel{540}}{ \cancel2}$

$= \large{270} \: cm$

By using Heron's formula

$\sf{ Area \: of \: triangle } = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies \: Area \: of \: triangle = \sqrt{270(270 - 120)(270 - 170)(270 - 250)} \\ \implies \: Area \: of \: triangle = \sqrt{270 \times 150 \times 100 \times 20} \\ \implies \: Area \: of \: triangle = \sqrt{81000000} \\ \implies \: Area \: of \: triangle = \sqrt{900 \times 9000} \\ \implies \: 9000 \: c {m}^{2}$