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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
(b) 6 cm
(c) 7 cm
(d) 8 cm



Answer -

In the figure, ABCD and AXYZ are squares
DY = 3 cm, AZ = 2 cm
 
DZ = DY + YZ
= DY + Z = 3 + 2 = 5 cm
In ∆ADZ, ∠2 = 90°
AD2 + AZ2 + DZ2 = 22 + 52 cm
= 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 = (5)2
∴ BX = 5 cm (a)

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