Question

Mark (✓) against the correct answer
∆ABC is an isosceles right triangle in which ∠A = 90° and BC = 6 cm. Then AB = ?

(a) $2\sqrt{2}\mathrm{cm}$
(b) $3\sqrt{2}\mathrm{cm}$
(c) $4\sqrt{2}\mathrm{cm}$
(d) $2\sqrt{3}\mathrm{cm}$

Answer 1

$$\begin{gathered} \left(b\right)3\sqrt{2}\mathrm{cm} \\ \begin{array}{l}\text{Here, AB}=\text{AC}\\ \text{In right angled isoceles triangle:}\\ {\text{BC}}^2={\text{AB}}^2+{\text{AC}}^2\\ {\text{=>BC}}^2=2{\text{AB}}^2\\ \text{=>}36=2{\text{AB}}^2\\ {\text{=>AB}}^2=\frac{3{\sout{6}}^{18}}{\sout{2}}\\ \text{=>AB=}\sqrt{18}\\ \text{=>AB=3}\sqrt{2}\text{cm}\end{array} \end{gathered}$$