In the figure, X is a point in the interior of square ABCD.AXYZ is also a square. If DY=3 cm and AZ=2 cm, then BY=
The correct option is C:7 cm
In the figure, ABCD and AXYZ are squares.
DY=3 cm, AZ=2 cm
DZ=DY+YZ
=DY+AZ=3+2=5 cm
In ΔADZ, ∠Z=90∘
AD2=AZ2+DZ2=22+52=4+25=29
In ∠ABX, ∠X=90∘
AB2=AX2+BX2
⇒AD2=AZ2+BX2 (∵ AB=AD, AX=AZ, sides of square)
⇒29=22+BX2
⇒ 29=4+BX2
⇒ BX2=29−4=25
⇒BX=5 cm
∴BY=BX+XY=5+2=7 cm [∵AXYZ is a square, AX=AZ=2 cm]