Question

In
the given figure ABC= 90° BD perpendicular AC .IfBD= 10 cm and AD=5cm, then find the value of CD.
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Answer 1

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Answer 2

The value of CD is 20cm.

Given: In the triangle ABC, ∠ABC = 90° and BD is perpendicular to AC.

To find: If BD = 10 cm and AD = 5cm, then find the value of CD.

Solution:

We are given,

∠ABC = 90° and ∠BDC = 90°

In ΔBDC

Let ∠BCD = x°

Now,

By using Angle Sum Property in ΔBDC, we get,

∠DCB = 90° - x°

We know that in a right angled triangle, if a perpendicular is drawn from the right angled vertex, it will divide the triangle into two similar triangles.

Therefore,

In ΔADB also,

∠ADB = x° and ∠BAD = 90° - x°

Now considering ΔBDC and ΔADB

∠BDC = ∠ ADB = 90°

∠BCD = ∠ADB = x° and

∠DCB = ∠BAD = 90° - x°

By A-A-A property, ΔBDC ~ ΔADB

Hence,

⇒ BD/CD = AD/BD

⇒ 10/CD = 5/10

⇒ 10/CD = ½

⇒ CD = 10 × 2

⇒ CD = 20

∴ CD = 20cm

Therefore, the value of CD is 20cm.

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