Question

In ΔABC, ∠B = 90°, AD = 17 cm, AB = 15 cm, CD = 12 cm, find AC.

Options

• 20 cm

• 24 cm

• 25 cm

• 30 cm

Answer 1

25 cm

Explanation:

In ΔABC, ∠B = 90°, AD = 17 cm, AB = 15 cm, CD = 12 cm.

Find AC.

Step 1: Find BD using triangle ABD:

In right triangle ABD:

AD² = AB² + BD²

17² = 15² + BD²

289 = 225 + BD²

BD² = 289 − 225

BD² = 64

BD = 8 cm

Step 2: Find BC.

BC = BD + DC

= 8 + 12

= 20 cm

Step 3: Use triangle ABC to find AC:

AC² = AB² + BC²

AC² = 15² + 20²

AC² = 225 + 400

AC² = 625

AC = `sqrt625`

AC ​= 25 cm