The corners of a square of side 'r' are cutoff so that a regular octagon remains. Then the length of each side of the resulting octagon is
Answers
Answer:
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Let ABCD be a square of side 2m. We form a regular octagon by cutting all four corners.
Let EF=FG=GH=HI=IJ=JK=KL=LE=x
By symmetry, AE=AL=BG=BF=CH=CI=DJ=DK=a
Using Pythagoras theorem in △ALE, we get
LE
2
=AL
2
+AE
2
x
2
=a
2
+a
2
=2a
2
⇒x=
2
a
And AB=AE+EF+FB⇒2=a+x+a→2a+x=2
Put the value of x, we get
2a+
2
a=2⇒a
2
(
2
+1)=2⇒a=
2
+1
2
∴x=
2
.
2
+1
2
=
2
+1
2
∴Length of each side of the octagon is
2
+1
2
m
Answer:
Let ABCD be a square of side 2m. We form a regular octagon by cutting all four corners.
Let EF=FG=GH=HI=IJ=JK=KL=LE=x
By symmetry, AE=AL=BG=BF=CH=CI=DJ=DK=a
Using Pythagoras theorem in △ALE, we get
LE
2
=AL
2
+AE
2
x
2
=a
2
+a
2
=2a
2
⇒x=
2
a
And AB=AE+EF+FB⇒2=a+x+a→2a+x=2
Put the value of x, we get
2a+
2
a=2⇒a
2
(
2
+1)=2⇒a=
2
+1
2
∴x=
2
.
2
+1
2
=
2
+1
2
∴Length of each side of the octagon is
2
+1
2
m