Question

A square and a regular hexagon have side of the same length. The perimeter of the square increased by 48 units will be equal to the perimeter of the hexagon. What is the x, the length of the side of the hexagon or square

Answer 1

The length of the side of the hexagon or square is 24 units.

Step-by-step explanation:

It is given that, a square and a regular hexagon have side of the same length.

The length is not given in the problem. So, let us assume the length of the side of hexagon or square as 'x'.

The additional information given is that, the perimeter of the square increased by 48 units will be equal to the perimeter of the hexagon.

• The perimeter of the square = 4 × length of the side.
• Then, the perimeter of the square increased by 48 units = (4x + 48).
• The perimeter of the hexagon = 6 × length of the side.
• Therefore, the perimeter of the hexagon = 6x.

To calculate the length x of square and hexagon :

Comparing both the perimeters of square and hexagon,

⇒ (4x + 48) = 6x

⇒ 48 = 6x-4x

⇒ 2x = 48

⇒ x = 48/2

⇒ x = 24 units.

The length of the side of the hexagon or square is 24 units.