Question

Assertion: The area of an isosceles triangle having base = 24 cm and each of the equal sides equal to 13 cm is 60 cm².
Reason: If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area $=\sqrt{s(s-a)(s-b)(s-c)}$.
(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:
$$\begin{gathered} \mathrm{Let}: \\ a=24\mathrm{cm},b=13\mathrm{cm}\mathrm{and}c=13\mathrm{cm} \\ s=\frac{a+b+c}{2}=\frac{24+13+13}{2}=25\mathrm{cm} \\ \mathrm{By}\mathrm{Heron}\text{'}\mathrm{s}\mathrm{formula},\mathrm{we}\mathrm{have}: \\ \mathrm{Area}\mathrm{of}\mathrm{triangle}=\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{25(25-24)(25-13)(25-13)} \\ =\sqrt{25\times 1\times 12\times 12} \\ =\sqrt{5\times 5\times 12\times 12} \\ =5\times 12 \\ =60{\mathrm{cm}}^2 \end{gathered}$$

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