Question

in triangle ABC, angle A=90degree,AB= 3cm, BC=5cm and AD perpendicular to BC. Then The length of AD is

Answer 1

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Answer 2

Answer:

The length of $AD=\frac{12}{5}=2.4 cm$

Step-by-step explanation:

Given ΔABC, ∠A=90°, AB=3cm, BC=5cm

AD is perpendicular to BC.

We have to find the length of AD

In ΔADB and ΔCAB

∠ADB=∠BAC   (each 90° given)

∠B=∠B              (common)

By AA similarity rule, ΔADB~ΔCAB

Hence, corresponding sides are in proportion

$\frac{DB}{AB}=\frac{AB}{CB}$

⇒ $\frac{DB}{3}=\frac{3}{5}$

⇒ $DB=\frac{9}{5}$

By Pythagoras theorem in ΔADB

$AB^2=AD^2+DB^2$

⇒ $3^2=AD^2+(\frac{9}{5})^2$

⇒ $AD^2=9-\frac{81}{25}=\frac{144}{25}$

⇒ $AD=\frac{12}{5}=2.4 cm$