Question

A wire in the shape of an equilateral triangle of
side 16 cm is rebent into a regular octagon. Each
side of the octagon is :
(a) 8 cm (b) 4 cm (c) 6 cm (d) 12 cm​

Answer 1

Step-by-step explanation:

Answer

If the side of the triangle be a cm, then

S=

4

a

3

3

or a

2

=

3

4S

and the perimeter of the triangle = 3a

∴Circumference of the circle = 3a

∴ If r be the radius of the circle, 2πr=3a

∴r=

2π

3a

∴ Area of the circle =πr

2

=π×

4π

2

9a

2

=

4π

9

×

3

4S

=

π

3

3

S

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Answer 2

Answer:

6 cm

Step-by-step explanation:

Here the side of equilateral triangle is X=16cm

Hence, total length of wire = perimeter of triangle

= X+X+X =3X =3(16) = 48 cm

Now wire is bent in shape of octagon.

Let, the side of octagon is Y cm.

Hence, perimeter of octagon

= total length of wire

So, 8Y=48

Y=48/8 =6cm

Hence length of side of octagon is 6 cm.