Question

In the given figure ∟ABC = 900
, BD⊥ AC ,AB=12cm , BC=9cm, CA=15cm

then the length of AD is

3.6 6.3

6.6 9.6​

Answer 1

Given:

∠ABC = 90°, BD⊥ AC, AB = 12cm, BC = 9cm, CA = 15cm

To find:

The length of AD

Solution:

It is given that BD⊥ AC

∴ ∠ADB = 90° . . .  (1)

In ΔABC and ΔADB, we have

∠BAC = ∠BAD . . . [common angle]

AB = AB . . . [common side]

∠ABC = ∠ADB = 90° . . . [from (1)]

∴ Δ ABC ~ Δ ADB . . . [By ASA for similarity]

We know that → The corresponding sides of the similar triangles are proportional to each other.

So, for the two similar triangles ΔABC and ΔADB, we have

$\frac{AB}{AD} = \frac{AC}{AB}$

$\implies AD = \frac{AB^2}{AC}$

on substituting the given values of AB = 12 cm and AC = 15 cm, we get

$\implies AD = \frac{12^2}{15}$

$\implies AD = \frac{144}{15}$

$\implies \bold{AD = 9.6\:cm}$

Thus, the length of AD is → 9.6 cm.

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