Question

Two sides of a triangle are of lengths 5 cm and 12 cm. If it's perimeter is 30 cm, find it's area.​

Answer 1

Perimeter of Triangle = Sum of all Sides

⇒ Perimeter of Triangle = 5 cm + 12 cm + x cm

⇒ Perimeter of Triangle = 17 cm + x cm

⇒ 30 cm = 17 cm + x cm

⇒ 30 cm - 17 cm = x cm

⇒ x = 13 cm

Semi Perimeter of Triangle = (5 cm + 12 cm + 13 cm)/2

⇒ Semi Perimeter of Triangle = (17 cm + 13 cm)/2

⇒ Semi Perimeter of Triangle = 30 cm/2

⇒ Semi Perimeter of Triangle(s) = 15 cm

By using Heron's formula :

Area of Triangle = √ [(s (s - a) (s - b) (s - c))]

⇒ Area of Triangle = √ [(15 cm (15 cm - a) (15 cm - b) (15 cm - c))]

⇒ Area of Triangle = √ [(15 cm (15 cm - 5 cm) (15 cm - 12 cm) (15 cm - 13 cm))]

⇒ Area of Triangle = √ [(15 cm (10 cm) (3 cm) (2 cm))]

⇒ Area of Triangle = √[900]

⇒ Area of Triangle = 30 cm²

Answer 2

Answer:

Area = 30 cm^2

Step-by-step explanation:

Perimeter of triangle = a+b+c

30 = 5 + 12 + c

30 = 17 + c

c = 30 - 17

c = 13 cm

area of triangle =

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

s = [a+b+c]/ 2

s = ( 12 +5 +13 )/ 2

s = 15

area of triangle =

$\sqrt{15(15 - 12)(15 - 5)(15 - 13)}$

$\sqrt{900}$

= 30 cm^2