Question

ABC is a right triangle, right angled at B, with AB = 3 cm and BC = 4 cm. BD is drawn perpendicular to the hypotenuse AC. Find the length of BD if AC = 5 cm
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Answer 1

Answer:

The answer will be BD = 2.4cm.

Step-by-step explanation:

Given things;

∆ABC and ∆ADB are right angled triangle, right angled at B and D respectively.

AB = 3cm

BC = 4cm

AC = 5cm

Now,

In ∆ABC and ∆ADB;

 ∠ABC =  ∠ADB;

 ∠A =  ∠A;

Thus, ∆ABC ~ ∆ADB ( AA criteria of similarity )

Thus, AB/ AD = AC/AB = BC/BD. (i)

Hence, AC/AB = BC/BD. (from eq. (i))

5/3 = 4/BD

BD = 12/5

BD = 12/5

= 2.4cm

That's all.