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Mathematics

In the given figure, ∠BAP = ∠DCP = 70°, PC = 6 cm and CA = 4 cm, then PD : DB is equal to:

  1. 5 : 3

  2. 3 : 5

  3. 3 : 2

  4. 2 : 3

In the given figure, ∠BAP = ∠DCP = 70°, PC = 6 cm and CA = 4 cm, then PD : DB is equal to: Similarity of Triangles, RSA Mathematics Solutions ICSE Class 10.

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Answer

Given,

∠BAP = ∠DCP = 70°

From figure,

∠BAP and ∠DCP are corresponding angles and since they are equal.

∴ AB ∥ CD.

By basic proportionality theorm,

⇒PDDB=PCCA⇒PDDB=64⇒PDDB=32⇒PD:DB=3:2.\Rightarrow \dfrac{PD}{DB} = \dfrac{PC}{CA} \\[1em] \Rightarrow \dfrac{PD}{DB} = \dfrac{6}{4} \\[1em] \Rightarrow \dfrac{PD}{DB} = \dfrac{3}{2} \\[1em] \Rightarrow PD : DB = 3 : 2.

Hence, option 3 is the correct option.

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