Take 2 metres long wire and cut 10% of the wire. Then cut 10% of the remaining wire.
Repeat this three times. Then measure the length of the wire.
Verify your length of the wire in each part using compound interest formula (Taking (-ve)
sign in the formula as this is depreciation method).
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Answer:
Total length of wire=10m
Let 'a' be length of part cut and bent into circle
∴2πr=a
r=
2π
a
Let (10−a) be length of part bent into equilateral triangle
∴3S=(10−a)
S=(
3
10−a
)
Combined area of two figures=πr
2
+
4
3
S
2
A=π(
4π
2
a
2
)+
4
3
(
3
10−a
)
2
A=
4π
a
2
+
36
3
(a
2
−20a+100)
A=(
4π
1
+
36
3
)a
2
−
9
5
3
a+
9
25
3
A
′
=2(
4π
1
+
36
3
)a−
9
5
3
=0
⇒a=
2π
1
+
18
3
9
5
3
=
(
2π
9
+
2
3
)
5
3
∴a=
9+π
3
10π
3
,10−a=
9+π
3
90
Wire must be cut in ration, a:10−a=π:3
3
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