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  • In Fig., if angle A = angle C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then find the lengths of PD and CD.

\\\text{In Fig., if }\angle A = \angle C, AB = 6 \; cm, BP = 15 \; cm, AP = 12 \; cm \; and \; CP = 4cm 

, then find the lengths of PD and CD.

 

 

Answers (1)

Answer: [PD=5cm, CD=2cm]

Given

: \angle A=\angle C,AB=6\; cm,BP=15\; cm

AP = 12 cm and CP = 4 cm

\text{In }\Delta APB\; and\; \Delta CPD

\angle A=\angle C                    

\angle APB=\angle DPC  \text{(Vertically opposite angle) }

\therefore \Delta APB \sim \Delta CPD \text{ [by AA similarity criterion]}

\Rightarrow \frac{AP}{CP}=\frac{PB}{PD}=\frac{AB}{CD}

     \frac{12}{4}=\frac{15}{PD}=\frac{6}{CD}

on taking first and second term we get

 PD=\frac{15 \times 4}{12}

PD=5\; cm

On taking first and last term we get

\frac{12}{4}=\frac{6}{CD}

CD=\frac{6 \times 4}{12}

CD=2\; cm

Posted by

infoexpert23

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