Question

In ΔABC, ∠B=90° and BD⊥AC. If AC=9cm and AD=3cm, then find BD.​

Answer 1

AC = 9cm ,AD = 3cm, CD = 9 - 3 = 6cm

triangle ABD is similar to triangle BDC

So,

AD:BD = BD: CD

BD^2 = AD × CD

BD^2 = 3×6 = 18

BD = √18 = 3√2 cm Answer

Answer 2

The length of the BD will be 6cm.

Given:

In ΔABC ∠B = 90°

BD⊥AC

AC= 9cm

AD= 3cm

To Find:

The length of BD.

Solution:

BD divides the right triangle ΔABC into two right triangles, ΔABD and ΔBDC. [Refer to the attached image]

In ΔABC according to Pythagoras Theorem,

$AB^{2} +BC^{2} = AC^{2}$-----(i)

In ΔABD,

$AB^{2} =BD^{2} +AD^{2}$

In ΔBDC,

$BC^{2} =BD^{2} +DC^{2}$

In eq (i) replacing $AB^{2}$ and $BC^{2}$ we get,

$BD^{2}+ AD^{2}+ BD^{2}+ DC^{2} =AC^{2}$

⇒$2BD^{2} =AC^{2} -AD^{2}$ $= 9^{2} -3^{2}$$=72$

⇒$BD= 6$

Hence, the length of BD is 6cm.

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