Question

The figure given alongside shows a square ABCD of side 40 cm. It is given that
E is a midpoint of AD, F is the midpoint of AE and FG is parallel to AB. If FG
is perpendicular to BC, intersecting AC and BE at Q and R, respectively, then
the length of QR is
a) 10 cm
b) 12 cm
c) 8 cm
d) 15 cm​

Answer 1

Answer:

In ΔAFQ, ∠FAQ = 45°

∴ tan45° = FQ/AF

⇒ FQ = 10 cm

Now, tan∠ABE = 1/2 [AE= 20 cm, AB = 40 cm]

∴ tan∠RBG = 2 [∵ ∠ABE + ∠RBG = 90°]

⇒RG/GB = 2  [GB = AF = (40÷4)cm = 10 cm]

∴ RG = 20 cm

∴ QR = (40 - 20 - 10) cm = 10 cm.                                      Ans. Option (a)

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