Question

In the given figure, angle ACB = 90° = angle ACD. If AB = 10 m, BC = 6 cm and AD = 17 cm, find :
(i) AC
(ii) CD

Answer 1

∆ ABD
∠ACB = ∠ACD = 90°
and AB = 10 cm, BC = 6 cm and AD = 17 cm

To find:
(i) Length of AC
(ii) Length of CD

Proof:

(i) In right-angled triangle ABC
BC = 6 cm, AB = 110 cm
According to Pythagoras Theorem,
AB² = AC² + BC²
(10)² = (AC)² + (6)²
100 = (AC)² + 36
AC² = 100 − 36 = 64 cm
AC² = 64 cm
∴ AC = `sqrt(8xx8)` = 8 cm

(ii) In right-angle triangle ACD
AD = 17 cm, AC = 8 cm
According to Pythagoras Theorem,
(AD)² = (AC)² + (CD)²
(17)² = (8)² + (CD)²
289 – 64 = CD²
225 = CD²
CD =`sqrt(15xx15)` = 15 cm