Question

Assertion : The sides of a triangle are $3\mathrm{cm},4\mathrm{cm}$ and $5cm$ . Its area is $6{\mathrm{cm}}^2$.

Reason : If $2s=(a+b+c)$, where $a,b,c$ are the sides of a triangle, then area $=\sqrt{(s-a)(s-b)(s-c)}$

Which of the following is correct?

• A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
• B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
• C. If Assertion is correct but Reason is incorrect.
• D. If Assertion is incorrect but Reason is correct.

Answer 1

The correct option is C

If Assertion is correct but Reason is incorrect.

Explanation for correct option :

Option (C):

Assertion : The sides of a triangle are $3\mathrm{cm},4\mathrm{cm}$ and $5cm$ . Its area is $6{\mathrm{cm}}^2$.

Give sides of triangle $3\mathrm{cm},4\mathrm{cm}$ and $5cm$.

By heron's formula

$$\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{3+4+5}{2} \\ s=6\mathrm{cm} \end{gathered}$$

Area of a triangle,

$$\begin{gathered} \text{Area}=\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{\left(6\right)(6-3)(6-4)(6-5)} \\ =\sqrt{\left(6\right)\left(3\right)\left(2\right)\left(1\right)}=6{\mathrm{cm}}^2 \end{gathered}$$

Hence, Assertion is true.

Reason : If $2s=(a+b+c)$, where $a,b,c$ are the sides of a triangle, then area $=\sqrt{(s-a)(s-b)(s-c)}$

As we know,

We can determine the area of triangle by using Heron's formula:

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

Where, $s=\frac{a+b+c}{2}$,

$2s=(a+b+c)$, where $a,b,c$ are the sides of a triangle,

Heron's formula in the reason is not correct since $s$ is missing there
So, the reason is not correct.
Therefore, Assertion is correct but Reason is incorrect.
Hence, option $\left(c\right)$ is correct answer.