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In the given figure, $∠$ CAB =90° and AD ⊥ BC. ΔBDA∿ ΔBAC. If AC = 75 cm, AB = 100 cm and BC = 125 cm, then AD is,

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2 cm

220cm

60 cm

23 cm

answer is C.

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Detailed Solution

Given figure is,
Question Image

It is given that the angle

∠ C A B = 90 °

.
Also,

A D ⊥ B C

, which means

∠ A D B = 90 °

As the angle,

∠ C A B

and

∠ A D B

are right angles.

\Rightarrow

∠ A D B = ∠ C A B

…… (1)
As per the figure given in the question, it can be concluded that the angle

∠ B

is the common angle.

\Rightarrow

∠ D B A = ∠ C B A

…… (2)
So, by the AA test of similarity, it is concluded that ΔBDA∿ ΔBAC.
Therefore, the ratio of corresponding sides of similar triangles is equal.

D A A C = A B C B

\Rightarrow AD = \frac{AC \times AB}{CB}

\Rightarrow AD = \frac{75 \times 100}{125}

\Rightarrow AD = 60 cm

Therefore, the value of AD is 60cm.
Hence, option 3 is correct.

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