Question

find the area of triangle whose sides are in the ratio 5:12:13 and its perimeter is 60cm

Answer 1

Hi friend ✋

Perimeter = 5x + 12x + 13x = 60

30x = 60

x = 2

5x = 10 cm

12x = 24 cm

13x = 26 cm

area by herons formula....

s = ( 10 + 24 + 26 )/ 2

= 30


$area = \sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{30 \times 20 \times 36 \times 34} \\ = \sqrt{734400} \\ = 856.97 cm^{2}$

Answer 2

$\huge\sf{\underline{\underline{Solution:}}}$

Given

Ratio of sides of a triangle = 5 : 12 : 13

Let the constant ratio be x

Sides of the triangle :

• a = 5x
• b = 12x
• c = 13x

Given perimeter = 60 cm

Semi perimeter of the triangle s = (a + b + c)/2

⇒ s = (5x + 12x + 13x)/2

⇒ s = 30x/2

⇒ s = 15x

Also, s = Perimeter/2 = 60/2 = 30 cm

⇒ s = 30

⇒ 15x = 30

⇒ x = 30/15 = 2

Sides of the triangle :

• a = 5x = 5 * 2 = 10 cm
• b = 12x = 12 * 2 = 24 cm
• c = 13x = 13 * 2 = 26 cm

Semi perimeter s = 15x = 15 * 2 = 30 cm

By using Heron's formula

Area of the triangle A = √[ s(s - a)(s - b)(s - c)

Substituting the value,

⇒ A = √[ 30(30 - 10)(30 - 24)(30 - 26) ]

⇒ A = √[ 30(20)(6)(4) ]

⇒ A = √14400

⇒ A = 120 cm²

Hence, area of the triangle is 120 cm².