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# In figure, ∠CAB = 90º and AD ⊥ BC. If AC = 75 cm, AB = 1 m and BD = 1.25 m, find AD. - CBSE Class 10 - Mathematics

ConceptSimilarity Examples and Solutions

#### Question

In figure, ∠CAB = 90º and AD ⊥ BC. If AC = 75 cm, AB = 1 m and BD = 1.25 m, find AD.

#### Solution

We have,
AB = 1 m = 100 cm, AC = 75 cm and BD = 125 cm

In ∆BAC and ∆BDA, we have

∠BAC = ∠BDA [Each equal to 90º] and, ∠B = ∠B

So, by AA-criterion of similarity, we have

∆BAC ~ ∆BDA

\Rightarrow \frac{BA}{BD}=\frac{AC}{AD}

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

\Rightarrow AD=\frac{125\times 75}{100}cm=93.75cm

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Solution In figure, ∠CAB = 90º and AD ⊥ BC. If AC = 75 cm, AB = 1 m and BD = 1.25 m, find AD. Concept: Similarity Examples and Solutions.
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