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Question

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=

A

5 cm

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B

6 cm

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C

7 cm

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D

8 cm

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Solution

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=294=25

BX=5 cm

BY=BX+XY=5+2=7 cm [AXYZ is a square, AX=AZ=2 cm]


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