Question

Assertion: The sides of a $\Delta ABC$ are in the ratio 2:3:4 and its perimeter is 36cm. Then, $ar\left(\Delta ABC\right)=12\sqrt{15}c{m}^2$

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

Which of the following is correct?

• A. A and R are true and R is the correct explanation of A.
• B. A and R are true and R is not the correct explanation of A.
• C. A is true and R is false.
• D. A is false and R is true.

Answer 1

The correct option is C

A is true and R is false.

Clearly, the given formula is wrong, So, Reason (R) is false.

Let the sides of $\Delta ABC$ be 2x, 3x and 4x cm.

Then,

$9x=36\Rightarrow x=4$

So, the sides are 8cm, 12cm and 16cm.

$\therefore s=18,(s-a)=10,(s-b)=6$ and (s - c) = 2

$\therefore$ Area $=\sqrt{18\times 10\times 6\times 2}$

$=\sqrt{6\times 3\times 5\times 2\times 6\times 2}$

$=12\sqrt{15}c{m}^2$

So, Assertion (A) is true and Reason (R) is false.