Question

ABCD is a rectangle in which AB=x+y and BC = x- y ,CD =10 ,AD =2 ,then values of x and y​

Answer 1

Answer:

AB=x,BC=y

xy=60

XA=XD,∠XAB=∠XDE,∠EXD=∠AXB

∴△XDE≅△XAB

∴ar△XDE=ar△XAB

Similarly

△YDF≅△YCB

∴ar△YDF=ar△YCB

Also, ∠FDY=∠FAB,∠DFY=DFY

∴△AFB∼△DFY

∴

DF

AF

=

FY

FB

=

DY

AB

DF

AF

=

FY

FB

=

2

x

x

⇒AF=2DF

AD=DF=y

Similarly DE=y

Now, ar△BEF=ar△YDF+ar△XDE+ar□DXYB+ar△DEF

=ar△YCB+ar△XAB+ar□DXYB+ar△DEF

=ar□ABCD+ar△DEF

=xy+

2

1

×DF×DE

=xy+

2

xy

=60+

2

60

=90