Question

The length of AB is ______.

Options

• 20 cm

• `10(sqrt3 - 1) cm`

• `10sqrt3  cm`

• `10(sqrt3 + 1) cm`

Answer 1

The length of AB is `bbunderline(10(sqrt3 + 1) cm)`.

Explanation:

The total base AB is split into two parts by the perpendicular line of height 10 cm:

• Left part: \[\frac{10}{\tan 45^\circ} = 10\text{ cm}\]

• Right part: \[\frac{10}{\tan 30^\circ} = 10\sqrt{3}\text{ cm}\]

Adding them together gives \[\text{AB} = 10 + 10\sqrt{3} = 10(\sqrt{3} + 1)\text{ cm}\].