Question

a wire 1m 68cm long is cut into two equal pieces. one piece is used to make a regular pentagon and the other is used to make a regular hexagin. find the difference in the lengths of the sides of the pentagon and hexagon formed.

Answer 1

Length of whole wire = 1m 68cm = 168cm
Length of each piece = 84cm

Length of one side of pentagon = 16.8cm
Length of one side of hexagon = 14cm
Difference = 2.8cm

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Answer 2

The difference in the lengths of the sides of the pentagon and hexagon formed is 2.8 cm.

To find :

The difference in the length of the sides of the pentagon and hexagon formed.

Given :

A wire of 1 m 68 cm.

Conversion of m to cm :

1 m = 100 cm

1 m 68 cm ⇒ 100 + 68 ⇒ 168 cm.

A wire of 168 cm is cut into two equal pieces :

i.e.,           $\frac{168}{2}$ = 84 cm

One piece is used to make a regular pentagon :

A regular pentagon has 5 sides.

One piece of regular pentagon is $\frac{84}{5}$ = 16.8 cm

Other piece is used to make a regular hexagon :

A regular hexangon has 6 sides.

Other piece of regular hexagon is $\frac{84}{6}$ = 14 cm.

Difference in the length of the sides of the pentagon and hexagon formed :

Length of the sides = Regular pentagon - Regular hexagon

                                 = 16.8 - 14

                                 = 2.8

Therefore, the length of the side is 2.8 cm.

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