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 =
A. 5 cm
B. 6 cm
C. 7 cm
D. 8 cm
Answers
Given : X is a point in the interior of square ABCD. AXYZ is also a square. If DY = 3 cm and AZ = 2 cm.
∠Z = 90° (Angle of a square , AXYZ)
Therefore, ∆AZD is a right angle triangle,
By using Pythagoras theorem,
AD² = AZ² + ZD²
AD² = AZ² + (ZY + DY)²
AD² = 2² + (2 + 3)²
[ZY = 2 cm , side of a square, AXYZ]
AD² = 4 + 5²
AD² = 4 + 25
AD = √29
In ∆AXB, right angle at x.
By using Pythagoras theorem :
AB² = AX² + XB²
√29² = 2² + XB²
[side of a square ABCD , AB = AD ]
29 = 4 + XB²
XB² = 29 - 4
XB² = 25
XB = 5 cm
Now,
BY = XB + XY
BY = 5 + 2
[XY = 2 cm , side of a square , AXYZ]
BY = 7cm
Hence, BY is 7 cm.
Option (C) 7 cm is correct.
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