Question

A square of side-
length 7.5m has the
same perimeter as a
regular hexagon
Find the side-length
(in m) of the
hexagon.​

Answer 1

Answer:

Side of hexagon = 5 m

Step-by-step explanation:

Perimeter of Square = 4 × 7.5

= 30 m

Perimeter of Hexagon = 30 m

Side of hexagon = 30/6

= 5 m

Answer 2

Answer:

The length of side of regular hexagon is equal to 5m.

Step-by-step explanation:

Given, length of the side of a square, $a=7.5m$

We know that the perimeter of a square is equal to the sum of all four sides of a square.

Consider that a is the length of side of the square.

∴   Perimeter of the square  $=4a$

                                             $= 4(7.5)\\ =30m$

Now, the perimeter of a regular hexagon is equal to sum of length of all six sides of the hexagon.

Consider b is the length of each side of a hexagon.

Perimeter of regular hexagon $=6b$  

Given, perimeter of Hexagon = perimeter of a square

⇒    $6b=30$

⇒     $b=\frac{30}{6}$

∴      $b=5m$

Therefore, the side-length of the hexagon is equal to 5m.