Question

Prove that÷

Area of a Triangle=√s(s-a)(s-b)(s-c)​

Answer 1

Answer:

Step-by-step explanation:

herons formula it come in standard 9

Perimeter of the triangle ABC is (a+b+c)/2

Area of triangle ABC = ½ (ah)  → (1)

Now we have find h in terms of a, b and c.

In right ΔADB, c2 = p2 + h2

In right ΔADC, b2 = q2 + h2

Here q = a – p

⇒ q2 = (a – p)2

= a2 – 2ap + p2

⇒ q2 + h2 = a2 – 2ap + p2 + h2

⇒ b2 = a2 + h2 – 2ap + p2

⇒ b2 = c2 – 2ap + p2

Solve this equation for p and substitute in equation (1) to get area of triangle formula.