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Asked by Topperlearning User 3rd October 2017, 3:20 PM
Answered by Expert
Answer:

begin mathsize 12px style left parenthesis straight i right parenthesis
AD over BD equals 3 over 2
Let space AD space equals space 3 straight x
Then space DB space equals space 2 straight x
AD over BD equals fraction numerator 3 straight x over denominator AD thin space plus space DB end fraction
equals fraction numerator 3 straight x over denominator 3 straight x space plus space 2 straight x end fraction
equals fraction numerator 3 straight x over denominator 5 straight x end fraction
equals 3 over 5

left parenthesis ii right parenthesis
In space increment space ADE space and space increment space ABC
angle space ADE space equals space angle space ABC space space space space left parenthesis corresponding space angles right parenthesis
angle space AED space equals space angle space ACB space space space space left parenthesis corresponding space angles right parenthesis
rightwards double arrow space increment space ADE space tilde space increment ABC
rightwards double arrow DE over BC equals AD over DB equals 3 over 5

left parenthesis iii right parenthesis
In space increment DEF space and space increment space CFB
angle space DEF space equals space angle space CFB space space space space space space left parenthesis Alternate space angles right parenthesis
angle space DFE space equals space angle space CFB space space space space space space left parenthesis Vertically space opposite right parenthesis
increment DEF tilde space increment space CFB space space space space space space space space left parenthesis AA space similarity right parenthesis

left parenthesis iv right parenthesis space
DE over BC equals DF over FC equals 3 over 5
rightwards double arrow fraction numerator DF over denominator DF space plus space FC end fraction equals 3 over 8
fraction numerator Area space of space increment space DFE over denominator Area space of space increment DEC end fraction space equals space fraction numerator begin display style 1 half end style cross times space DE space cross times space straight h over denominator 1 half cross times space DC space cross times space straight h end fraction
DF over DC equals 3 over 8 end style

Answered by Expert 3rd October 2017, 5:20 PM
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