Question

side of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm what will be the area

Answer 1

Given, sides of triangle are in the ratio 12 : 17 : 25

Let the constant be x

Let the sides in the ratio be 12x, 17x and 25x

Given, perimeter is 540cm

According to the question,

12x + 17x + 25x = 540

➾ 54x = 540

➾ x = 10

∴ 1st side of traingle ➾ 12x

➾ 12 × 10

➾ $\green{\boxed{\green{\boxed{\red{\textsf{120\:cm}}}}}}$

∴ 2nd side of triangle ➾ 17x

➾ 17 × 10

➾ $\green{\boxed{\green{\boxed{\red{\textsf{170\:cm}}}}}}$

∴ 3rd side of triangle ➾ 25x

➾ 25 × 10

➾ $\green{\boxed{\green{\boxed{\red{\textsf{250\:cm}}}}}}$

Semiperimeter = $\dfrac{540}{2}$ = 270cm

Now, by using Heron's formula, we will find out the area of the triangle

√s(s - a) (s - b) (s - c)

➾ √270(270 - 120) (270 - 170) (270 - 250)

➾ √270(150) (100) (20)

➾ 9000cm²

Answer 2

Solution :

Let sides be a = 12x cm , b = 17x cm and c = 25x cm , Where x is  any number

We have given ,

Perimeter = 540 cm

⇒ a + b = c = 540

⇒ 12x + 17x + 25x = 540

⇒ 29x + 25x = 540

⇒ 54x = 540

⇒ x = 540/54

⇒ x = 10

Substitute the value of x

12x

⇒ 12 × 10

⇒ 120 cm

17x

⇒ 17 × 10

⇒ 170 cm

25x

⇒ 25 × 10

⇒ 250 cm

Finding area of triangle

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

Semi - perimeter (S) = Perimeter/2

⇒ 540/2

⇒ 270 cm

Putting the values in the above formula

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

⇒ $\sqrt{270 * 150 * 100 * 20}$

⇒ $\sqrt{(27 * 15 *12) * (10)^5}$

⇒ $\sqrt{(27 * 3) * (10)^6}$

⇒ $\sqrt{81 * (10)^6}$

⇒ $\sqrt{81} * \sqrt{(10)^6}$

⇒ $\sqrt{(9) * (10^3)}$

⇒ $9000 cm^2$

Therefore , the area of the triangle is 9000 cm^2