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Question

Consider the triangle ABC shown in the following figure where BC=12cm,DB=9cm, CD=6cm and BCD=BAC.
What is the ratio of the perimeter of ADC to that of BDC?
299092_8092bfd2b9f34b84b7f279f4ff996ff4.png

A
79
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B
89
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C
69
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D
59
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Solution

The correct option is A 79
In BCD and ABC,
DBC=ABC ..... (Common angle)
BCD=BAC ....... (Given)
BC=BC ...... (Common side)
BCDABC ........ (Using ASA Rule)
ACDC=BCBD=ABBC
ABBC=BCBD
AB12=129
AB=16
Similarly,
ACDC=BCBD
AC6=129
AC=8
Hence, AD=7 and AC=8Therefore,
Perimeter of ADCPerimeter of BDC
=6+7+89+6+12
=2127
=79

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