In the given figure, if AB = 8 cm, AC = 10 cm, ∠ABD = 90o and AD = 17 cm, then the measure of (CD + AC) is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 19 cm.
ABC and ABD are right-angled triangles.
In triangle ABD:
AD2 = AB2 + BD2
⇒ 172 = 82 + BD2
⇒ BD2 = 289 - 64
⇒ BD = 15 cm
In triangle ABC:
AC2 = AB2 + BC2
⇒ 102 = 82 + BC2
⇒ BC2 = 100 - 64
⇒ BC = 6 cm
Hence,
CD = BD - BC = 15 - 6 = 9 cm
Now, (CD + AC) = 9 + 10 = 19 cm