Question

The area of a triangle is 216cm^2 and its sides are in ratio 3 : 4 : 5. Find the perimeter of the triangle.​

Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

The area of a triangle is 216 cm² & it's sides are in ratio 3:4:5.

$\underline{\bf{Explanation\::}}$

Let the ratio of sides of a triangle be r

• 1st side, (a) = 3r cm
• 2nd side, (b) = 4r cm
• 3rd side, (c) = 5r cm

$\underline{\mathcal{USING\:BY\:HERON'S\:FORMULA\::}}$

⇒ Semi - perimeter = Side + Side + Side/2

⇒ Semi - perimeter = 3r + 4r + 5r/2

⇒ Semi - perimeter = 12r/2

⇒ Semi - perimeter = 6r

&

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

⇒ 216 = √6r(6r - 3r)(6r - 4r)(6r - 5r)

⇒ 216 = √6r(3r)(2r)(r)

⇒ 216 = √36r^4

⇒ 216 = 6r²

⇒ r² = 216/6

⇒ r² = 36

⇒ r = √36

⇒ r = 6 cm

Now,

• 1st side of Δ = 3r = 3×6 = 18 cm
• 2nd side of Δ = 4r = 4×6 = 24 cm
• 3rd side of Δ = 5r = 5×6 = 30 cm

As we know that formula of the perimeter of triangle;

$\boxed{\bf{Perimeter \:of\:\triangle = Side + Side +Side}}$

→ Perimeter of Δ = 18 cm + 24 cm + 30 cm

→ Perimeter of Δ = 72 cm

Thus,

The Perimeter of the triangle will be 72 cm .