Question

find the area of a triangle which are 9 cm and 12 cm and the perimeter is 42 cm?

Answer 1

Answer:

21cm

Step-by-step explanation:

if A=9cm,B=12cm

A+B+C=42cm

C=(42-A-B)cm=(42-9-12)cm

C=21cm

Answer 2

Answer: i have given a step by step explanation below friend.

Step-by-step explanation:

Step 1 :

Given , 2 sides of the triangle Are 9cm and 12 cm. The another side’s value is not given, so let’s name it as “ c ”.

According To perimeter concept, perimeter = the sum of the sides.

So, 42 = 9 + 12 + c

42 = 21 + c

42 - 21 = c

= 21 = c

Therefore, the value of “ c ” is 21 cm.

Step 2 :

We have found the value of all the 3 sides. Now, we have to find the semiperimeter of the triangle.

Semiperimeter or S = $\frac{a+b+c}{2}$

So, S = $\frac{9 + 12 + 21 }{2}$

= $\frac{42}{2} = 21$

Therefore, the semiperimeter of the triangle is 21.

Step 3 :

We have found the semiperimeter. Now we have to apply the Heron’s formula.

Δ (delta) = $\sqrt{s(s-a)(s-b)(s-c)}$

We already know that a = 9 , b = 12 and c = 21,

⇒ Δ (delta) = $\sqrt{21(21-9)(21-12)(21-21)}$

= $\sqrt{21(12)(9)(0)}$

= 21 × 12 × 9 × 0

By prime factorisation = 3 × 7 × 2 × 2 × 3 × 3 × 3 × 0

= 3 × 3 × 2 × 7 × 0

= 3 × 2 × 7 × 0

= 3 × 2 × 0

= 6 × 0

= 0

Therefore, the area of the triangle is 0 or not defined.

Hope it’s useful friend..

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