Question

Abc is a triangle which is right angled at a and a perpendicular ad is drawn on the hypotenuse bc. If bc = 8 and ad = 3, then what is the value of ab

Answer 1

Answer:

AB=6

Explanation:

As AD is drawn perpendicular to BC in right angled ΔABC, it is apparent that ΔABC is right angled at ∠A as shown below (not drawn to scale).
 
As can be seen ∠B is common in ΔABC as well as ΔDBA (here we have written two triangles this way as ∠A=∠D, ∠B=∠B and ∠C=∠BAD) - as both are right angled (obviously third angles too would be equal) and therefore we have

ΔABC≈ΔDBA and hence

BCAB=ABBD=ACAD..............(1)

therefore, we have BCAB=ABBD or

AB2=BC×BD=9×4=36

Hence AB=6



P dilip_k

Jan 7, 2017

drawn

Given that ΔABC is right angled and AD is drawn perpendicular to BC . So ∠BAC is right angle.

Given BC=9cmandBD=4cm→CD=BC−BD=5cm

In ΔABCandΔABD

∠ABD=∠ABC

∠ADB=∠BAC=right angle

∠BAD=∠ACD(remaining)

So ΔABCandΔABD are similar

Hence

ABBC=BDAB

⇒AB2=BD×BC=4×9=36

⇒AB=√36cm=6cm

Answer 2

Ye hi Ho Sakta hae bass