Question

Why couldn’t Annie prepare good coffee?
This question is from DAV class 8th chapter (A bad Dream)

Answer 1

Answer:

Lets draw altitude from A to BC such that it meets BC at D, angles are ΔADC,∠D=90

o

⇒AD

2

+DC

2

=AC

2

⇒AD

2

+(BD+BC)

2

=AC

2

⇒AD

2

+BD

2

+BC

2

+2BD.BC=AC

2

………….(1)

In ΔADB,∠D=90

o

⇒AD

2

+BD

2

=AB

2

Substituting in equation (1)

⇒AD

2

+BD

2

+BC

2

+2BD.BC=AC

2

⇒AB

2

+BC

2

+2BD.BC=AC

2

as in ΔADB,∠DAB=∠45

o

⇒AD=DB(opposite sides are equal)

⇒AB

2

+BC

2

+2BD×BC=AC

2

⇒AB

2

+BC

2

+2AD×BC=AC

2

⇒AB

2

+BC

2

+4[

2

1

AD×BC]=AC

2

⇒AB

2

+BC

2

+4(ΔABC)=AC

2

∴ Hence proved.