Question

In ΔABD, AB ⊥ BD and AC = BD. If AB = 4 cm, BC = 2 cm, find AD.

Answer 1

Given that in ΔABD, AB ⊥ BD, AC = BD, AB = 4 cm, BC = 2 cm as shown below –

In right-angled triangle ABC

AC² = AB² + BC²

= 4² + 2²

= 16 + 4

= 20

⇒ AC = `sqrt(20)` cm

Since AC = BD so, BD = `sqrt(20)` cm

Now, in right-angled triangle ABD

AD² = AB² + BD²

= `4^2 + sqrt(20)^2`

= 16 + 20

= 36

⇒ AD = `sqrt(36)` = 6 cm

Hence, 6 cm is the required.