In Fig. 10.140, 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 =

∠Z = 90° (Angle of square)

Therefore, AZD is a right angle triangle,

By Pythagoras theorem,

AD² = AZ² + ZD²

AD² = 2² + (2+3)²

AD² = 4 + 25

AD = √29

In AXB, with​X as right angle,

By Pythagoras theorem,

AB² = AX² + XB²

XB² = 29-4

XB = 5

BY = XB + XY

= 5 + 2

= 7cm