Question

ABC is an isosceles triangle right angled at C with AC = 4 cm. Find the length of AB.

Answer 1

∆ABC is an isosceles triangle right angled at C.

∴ BC = AC (In an isosceles triangle, two sides are equal)

⇒ BC = 4 cm (AC = 4 cm)

In right ∆ABC,

$$\begin{gathered} {\mathrm{AC}}^2+{\mathrm{BC}}^2={\mathrm{AB}}^2\left(\mathrm{Pythagoras}\mathrm{theorem}\right) \\ \Rightarrow {\mathrm{AB}}^2={\left(4\right)}^2+{\left(4\right)}^2 \\ \Rightarrow {\mathrm{AB}}^2={\left(4\right)}^2\times 2 \\ \Rightarrow \mathrm{AB}=4\sqrt{2}\mathrm{cm} \end{gathered}$$

Thus, the length of AB is $4\sqrt{2}\mathrm{cm}$.