Question

*Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 16 cm and 9 cm. Find the length of the altitude.*

1️⃣ 7 cm
2️⃣ 12 cm
3️⃣ 10 cm
4️⃣ 14 cm​

Answer 1

Answer:

12cm (Option-2)

Step-by-step explanation:

Let Triangle is ABC (B=90 degree) and let BD=x is altitude.

Now, AD=9cm and DC=16cm

let angle DCB is theta then angle DBC=90-theta and angle DBA=theta,

Now in triangle ADB and DBC

tan(theta)=9/x and tan(theta)=x/16,

Therefore, 9/x = x/16, implies, x² = 9*16

therefore,

x=12cm is your answer!