Question

In ΔABD, AB ⊥ BD and AC = DB. AB = 4 cm, BC = 2 cm.

∴ AD = ______

Options

• `sqrt(20)` cm

• 8 cm

• 7 cm

• 6 cm

Answer 1

AD = 6 cm

Explanation:

In ΔABD, AB ⊥ BD and AC = DB. AB = 4 cm, BC = 2 cm.

We need to find AD.

Find AC using right triangle ABC:

AC² = AB² + BC²

AC² = 4² + 2²

AC² = 16 + 4

AC² = 20

AC = `sqrt(20)`

Use right triangle ABD to find AD:

AD² = AB² + BD²

AD² = 4² + `(sqrt(20))^2`

AD² = 16 + 20

AD² = 36

AD = `sqrt(36)`

AD = 6 cm