Length and breadth of a rectangle are 8 cm and 6 cm respectively The rectangle is cut on its four ve...........

Quantitative Aptitude (CGL) Coordinate Geometry

Length and breadth of a rectangle are 8 cm and 6 cm respectively. The rectangle is cut on its four vertices such that the resulting figure is a regular octagon. What is the side (in cm) of the octagon?

3(√11) – 7

5(√13) – 8

6(√11) – 9

4(√7) – 11

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Explanation:

Let ABCD is the rectangle whose AB =8 cm, BC=6cm,CD=8cm, and DA=6cm. E,F,G,H are the middle points of AB, BC, CD, and DA respectively. M,N,O,P,Q,R,S,T are the vertices of the regular octagon that formed ,and point M is on the line AE , other points N,O,P etc are on EB, BF, FC so on. Now MN=NO=OP=PQ=QR=RS=ST=TM= 2x .Then ME=x,
As AE=8/2= 4cm , AM=4-x
Similarly AT=3-x ,and TM=2x
As triangle ATM is a right triangle TM^2=AM^2+AT^2,
Or, (2x)^2=(4-x)^2+(3-x)^2
Or, 4x^2=16–8x+x^2+9–6x+x^2
Or, 2x^2+14x-25=0
Or,x=[-14±√{14^2–4×2×(-25)}]/(2×2)
Or, x={-14±√(196+200)}/4
Or, x=(-14±√396)/4
Or x=(-14±19.9)/4
Or x=5.9/4 …..Negative value discarded .
Or, x= 1.47 cm
So, ME =x=1.47 cm
MN=NO=…= 2x=2×1.47 = 2.94cm
Sides of the regular octagon is 2.94 cm
2.94=3(√11) – 7