#### Question

For finding AB and BC with the help of information given in the figure, complete following activity.

AB = BC ..........

\[\therefore \angle BAC = \]

\[ \therefore AB = BC =\] \[\times AC\]

\[ =\] \[\times \sqrt{8}\]

\[ =\] \[\times 2\sqrt{2}\]

=

#### Solution

In ∆ABC,

∠B = 90^{∘}, AC =\[\sqrt{8}\] AB = BC, ∴ ∠A = ∠C = 45^{∘}

By 45^{∘ }− 45^{∘} − 90^{∘} theorem,

\[AB = BC = \frac{1}{\sqrt{2}} \times AC\]

\[ = \frac{1}{\sqrt{2}} \times \sqrt{8}\]

\[ = \frac{1}{\sqrt{2}} \times 2\sqrt{2}\]

\[ = 2\]

Hence, AB = 2 and BC = 2.

Hence, the completed activity is

AB = BC .......... Given

\[\therefore \angle BAC = {45}^o \]

\[ \therefore AB = BC = \frac{1}{\sqrt{2}} \times AC\]

\[ = \frac{1}{\sqrt{2}} \times \sqrt{8}\]

\[ = \frac{1}{\sqrt{2}} \times 2\sqrt{2}\]

\[ = 2\]

Is there an error in this question or solution?

Solution For Finding Ab and Bc with the Help of Information Given in the Figure, Complete Following Activity. Ab = Bc .......... Concept: Pythagoras Theorem.