Question

In ΔABC, AD is an altitude and ∠A is right angle. If AB =√20, BD=4, CD = ....,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 5
(b) 3
(c) √5
(d) 1

Answer 1

In the above question we will apply Geometric Mean Theorem.

According to this theorem,

If an altitude divides its hypotenuse in p and q and let length of altitude h.

Then h can be given as following

$h=\sqrt{pq}$

using above theorem and Pythagoras theorem

we got CD = Q =1

Hence option d is correct

see the attachment

Answer 2

In ∆ABC ,

<A = 90° , AD = y is the altitude .

AB = √20 , BD = 4

i ) In ∆ADB , <ADB = 90°

By Pythagorean theorem ,

AB² = BD² + AD²

( √20 )² = 4² + y²

20 - 16 = y²

y² = 4

y = 2

ii ) We know that ,

In ∆BAC , <A = 90° ,

D is a point on BC such that

AD perpendicular to BC.

AD² = BD × DC

y² = 4 × x

2² = 4 × x

4/4 = x

x = 1

Therefore ,

x = CD = 1

Option ( d ) is correct.

I hope this helps you.

: )