Question

In the quadrilateral ABCD, ∠B = 90°, ∠ACD = 90°, AB = 3 cm, BC = 4 cm, CD = 12 cm, find AD.

Options

• 13 cm

• 15 cm

• 17 cm

• 14 cm

Answer 1

13 cm

Explanation:

First find AC in right triangle ABC:

`AC = sqrt(AB^2 + BC^2)`

= `sqrt(3^2 + 4^2)`

= `sqrt(9 + 16)`

= `sqrt(25)`

= 5 cm

Now in right triangle ACD (since ∠ACD = 90°):

`AD = sqrt(AC^2 + CD^2)`

= `sqrt(5^2 + 12^2)`

= `sqrt(25 + 144)`

= `sqrt(169)`

= 13 cm