Question

Assertion: The area of an isosceles triangle having base = 8 cm and each of the equal sides = 5 cm is 12 cm².
Reason: The area of an isosceles triangle having each of the equal sides as a and base = b is $\frac{1}{4}b\sqrt{4a^2-b^2}$.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

Assertion:
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{isosceles}\mathrm{triangle}=\frac{b}{4}\sqrt{4a^2-b^2} \\ \mathrm{Here}, \\ a=5\mathrm{cm}\mathrm{and}b=8\mathrm{cm} \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \frac{8}{4}\times \sqrt{4(5{)}^2-8^2} \\ =2\times \sqrt{100-64} \\ =2\times \sqrt{36} \\ =2\times 6 \\ =12{\mathrm{cm}}^2 \end{gathered}$$

Hence, Assertion is true.

Reason:
Area of an isosceles triangle having each of the equal sides as a and base as b is $\frac{1}{4}b\sqrt{4a^2-b^2}$.
Hence, it is true.