Question

Given three sticks of lengths 10 cm, 5 cm and 3 cm. A triangle is formed using the sticks,
then area of the triangle will be

Answer 1

No triangle is formed!

Step-by-step explanation:

Let us assume the three sides of the triangle as:

• a = 10 cm
• b = 5 cm
• c = 3 cm

According to the question, we can find the area of the triangle by using Heron's formula. According to this formula,

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

Here 's' denotes semi perimeter.

Formula to find semi-perimeter:

➪ s = (a + b + c) / 2

➪ s = (10 + 5 + 3) / 2

➪ s = 18 / 2

➪ s = 9

Now, by using Heron's formula, we get:

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

$\implies \: A = \sqrt{9(9-10)(9-5)(9-3)}$

$\implies \: A = \sqrt{9(-1)(4)(6)}$

$\implies \: A = \sqrt{-216}$

We can't find the square root of a negative integer.

Therefore, the triangle has no area and we can't form a triangle with the given sticks (False).