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a square and a regular hexagon have sides of the same length. the perimeter of the square increased by 32 units will be equal to the perimeter of the hexagon. what is x, the length of a side of the hexagon or square?



Answer :

The length of a side of the hexagon or square is - 16 units

  • A square has four equal sides and four equal angles. The angles of square are at right angles or 90°.
  • If all six sides are equal, then it is called a regular hexagon. The perimeter of the regular hexagon is defined as the sum of all the sides of a hexagon.

The length of a side of the hexagon or square = x

The perimeter of the square = 4 × lengths of its side

                                               = 4x

The perimeter of the hexagon = 6 × lengths of its side

                                                  = 6x

According to the question,

                                           4x + 32 = 6x

                                       ⇒ 6x - 4x = 32

                                       ⇒  2x = 32

                                       ⇒  x = 16

So, the length of a side of the hexagon or square is - 16 units.

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