GATE 2024 EE – Question 7
In the following figure,
CD = 5 cm, BE = 10 cm, AE = 12 cm,
∠DAB = ∠DCB, and ∠DAE = ∠DBC = 90°
Points AFCD create a rhombus.
The length of BF (in cm) is
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Correct answer: (A) 3
Explanation
In right triangle $DAE$ (right angle at $A$), $AD=CD=5$ (side of the rhombus) and $AE=12$, so $DE=\sqrt{25+144}=13$. $D$, $B$, $F$, $E$ lie on one line, so $DB=DE-BE=13-10=3$. The diagonals of a rhombus bisect each other at $B$, so $BF=DB=3$ cm.