Please solve

Asked by Divyaa | 26th Mar, 2017, 01:38: PM

Expert Answer:

begin mathsize 16px style In space triangle ADE space and space triangle ABC comma
AD over AB equals AE over AC equals 1 third left parenthesis given right parenthesis
angle DAE equals angle BAC space left parenthesis common space angle right parenthesis
rightwards double arrow triangle ADE tilde triangle ABC space left parenthesis SAS space criterion space of space similarity right parenthesis
rightwards double arrow fraction numerator straight A left parenthesis triangle ADE right parenthesis over denominator straight A left parenthesis triangle ABC right parenthesis end fraction equals open parentheses 1 third close parentheses squared space
space space space space space space space space space space.... left parenthesis since space ratio space of space the space areas space are space equal space to space the space ratio space of space the space squares space of space the space corresponding space sides right parenthesis
rightwards double arrow fraction numerator straight A left parenthesis triangle ADE right parenthesis over denominator straight A left parenthesis triangle ABC right parenthesis end fraction equals 1 over 9
rightwards double arrow straight A left parenthesis triangle ADE right parenthesis equals 1 over 9 straight A left parenthesis triangle ABC right parenthesis
To space find space straight A left parenthesis triangle ABC right parenthesis colon
Using space the space area space formula comma space
straight A left parenthesis triangle ABC right parenthesis space equals space open vertical bar fraction numerator 4 left parenthesis 5 minus 2 right parenthesis plus 1 left parenthesis 2 minus 6 right parenthesis plus 7 left parenthesis 6 minus 5 right parenthesis over denominator 2 end fraction close vertical bar
rightwards double arrow straight A left parenthesis triangle ABC right parenthesis equals space open vertical bar fraction numerator 12 minus 4 plus 7 over denominator 2 end fraction close vertical bar
rightwards double arrow straight A left parenthesis triangle ABC right parenthesis equals space 15 over 2 equals 7.5 space sq space units
So comma space straight A left parenthesis triangle ADE right parenthesis equals 1 over 9 cross times 7.5 equals 5 over 6 space sq space units
Hence comma space straight A left parenthesis triangle ADE right parenthesis space is space 5 over 6 space sq space units space and space straight A left parenthesis triangle ADE right parenthesis equals 1 over 9 straight A left parenthesis triangle ABC right parenthesis. end style

Answered by Rebecca Fernandes | 26th Mar, 2017, 09:22: PM