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In the given figure, ∠CAB = 90° and AD ⟂ BC. If AC = 75 cm, AB = 1 m and BC = 1.25 m, then AD equals:

  1. 50 cm

  2. 60 cm

  3. 65 cm

  4. 70 cm

In the given figure, ∠CAB = 90° and AD ⟂ BC. If AC = 75 cm, AB = 1 m and BC = 1.25 m, then AD equals: Similarity of Triangles, RSA Mathematics Solutions ICSE Class 10.

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Answer

Given,

∠CAB = 90°

AC = 75 cm = 0.75 m

AB = 1 m

BC = 1.25 m

In ΔCAB and ΔADB,

∠CAB = ∠ADB = 90° [AD ⟂ BC]

∠CBA = ∠ABD [Common angle]

∴ ΔCAB ∼ ΔADB by AA similarity. Then ratios of corresponding sides are equal:

⇒ACAD=BCAB⇒ACBC=ADAB⇒0.751.25=AD1⇒AD=0.751.25⇒AD=0.6 m.\Rightarrow \dfrac{AC}{AD} = \dfrac{BC}{AB} \\[1em] \Rightarrow \dfrac{AC}{BC} = \dfrac{AD}{AB} \\[1em] \Rightarrow \dfrac{0.75}{1.25} = \dfrac{AD}{1} \\[1em] \Rightarrow AD = \dfrac{0.75}{1.25} \\[1em] \Rightarrow AD = 0.6 \text{ m.}

AD = 0.6 m = 60 cm.

Hence, option 2 is the correct option.

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