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प्रश्न
In figure, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then PD = ______ and CD = ______.
रिकाम्या जागा भरा
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उत्तर
In figure, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then PD = 5 cm and CD = 2 cm.
Explanation:
Triangles ABP and CDP are similar (∠A = ∠C and ∠APB = ∠CPD).
So `(AB)/(CD) = (BP)/(PD) = (AP)/(CP)`.
Since `(AP)/(CP) = 12/4 = 3`, we have
`6/(CD) = 3`
⇒ CD = 2 cm
And `15/(PD) = 3`
⇒ PD = 5 cm
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