Question

What is the length of BC in the given figure?

• A. $2\sqrt{2}$ units
• B. 4 units
• C. $4\sqrt{2}$ units
• D. $\sqrt{2}$ units

Answer 1

The correct option is B

4 units

$△$ ABC is an isosceles triangle.

$\angle$ ABO = ${45}^{\circ }$

$\therefore$ $△$ AOB is a 45-45-90 triangle and the ratio of their sides = 1 : 1 : $\sqrt{2}$

Let AB = $x\sqrt{2}$, OB = OA = x

$\Rightarrow$ $2\sqrt{2}$ = $x\sqrt{2}$

$\Rightarrow$ x = 2

$\Rightarrow$ AO = OB = 2

Similarly AO = OC = 2

BC = OC + OB

Hence, The length of BC = 2 + 2 = 4 units