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Question

In ABC,BAC=90o,ADBC,BD=4cm,DC=5cm, Find x and y.
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Solution

It is given that BAC=900 and ADBC

Also, ABD and CBD are similar right angled triangle, thus with AD=y cm, BC=5 cm and DC=5 cm, we have,

AD2=BC×DCy2=4×5y2=20y=20y=25

Similarly, ABC and DBA are similar right angled triangle, thus with AB=x cm, BC=9 cm and BD=4 cm, we have,

AB2=BC×BDx2=9×4x2=36x=36x=6

Hence, x=6 cm and y=25 cm.

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