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In the given figure, $∠$ ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, then the value of BCis,

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8cm

8.1cm

8.2cm

8.3cm

answer is B.

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Detailed Solution

Given figure is,
969183

Here, AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm and BD ⊥ AC.
We know,
In a right-angled triangle, if the triangles are similar, then the corresponding sides are in proportional.
In

Δ A B C

,and

Δ B D C

∠ A B C = ∠ B D C Both 90 ° ∠ A C B = ∠ B C D common angle Δ A B C ~ Δ B D C by AA similarity

It is clear that the triangles are similar,
So, the corresponding sides are in the same ratio.
Now,

A B B C = B D D C

5.7 B C = 3.8 5.4 ⇒ B C = 5.7 × 5.4 3.8 ⇒ B C = 8.1 cm

The value of side BC is

8.1

cm.
Therefore, option 2 is correct.

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