Question

Assertion : The side of an equilateral triangle is 6 cm , then the area of the triangle is 9cm² Reason : All the sides of an equilateral triangle are equal.

a. Both assertion and reason are true and reason is the correct explanation of assertion.

b. Both assertion and reason are true but reason is not the correct explanation of assertion.

c. Assertion is true but reason is false.

d. Assertion is false but reason is true.​

Answer 1

Step-by-step explanation:

correct answer is (b) yes the correct answer

Answer 2

Given assertion:

Side of the equilateral triangle$\[ = 6cm\]$.

Area of the equilateral triangle$\[ = 9c{m^2}\]$

Check whether the assertion is true or not.

Know that,

Area of the equilateral triangle$\[ = \frac{{\sqrt 3 }}{4} \times \[{\left( {Side} \right)^2}\]\]$

                                                  $\[\begin{array}{l} = \frac{{\sqrt 3 }}{4} \times 6 \times 6\\ = 9\sqrt 3 c{m^2}\end{array}\]$

Observe that, the area calculated for the equilateral triangle having side $6cm$ i.e.,$\[9\sqrt 3 c{m^2}\]$ is not equal to the given area of the equilateral triangle i.e., $\[ 9c{m^2}\]$.

Therefore, the given assertion is NOT TRUE.

Check whether the reason is true or not.

Reason: All the sides of an equilateral triangle are equal.

Understand that the given reason is TRUE as all the sides and all the interior angles of an equilateral triangle are equal.

Hence, the Assertion is False but the Reason is true.