Question

Mark (✓) against the correct answer
∆ABC is an isosceles triangle with ∠C = 90° and AC = 5 cm. Then, AB = ?

(a) 2.5 cm
(b) 5 cm
(c) 10 cm
(d) $5\sqrt{2}\mathrm{cm}$

Answer 1

$$\begin{gathered} \left(d\right)5\sqrt{2}\mathrm{cm} \\ \begin{array}{l}\text{In right angled isoceles triangle, right angled at C,}AC\mathrm{is}\mathrm{equal}\mathrm{to}BC\mathrm{and}AB\text{is the}hypotenuse.\\ \begin{array}{l}\\ \begin{array}{l}{\text{AB}}^2={\text{AC}}^2+{\text{BC}}^2\\ {\text{=5}}^2+5^2\\ \text{=50}\\ \therefore \text{AB=}\sqrt{2\times 25}=5\sqrt{2}\text{cm}\end{array}\\ \\ \end{array}\end{array} \end{gathered}$$