consider a square and a regular pentagon. one side of the square is 6 feet longer than a side of the pentagon, and the figures have the same perimeter. what are the lengths of the sides of each figure?
side of pentagon --- x
side of square --- x+6
solve
5x = 4(x+6)
What is the perimeter of the Pentagon with side 3.2cm?
29 feet 30 feet 28 feet or 27 feet
To find the lengths of the sides of each figure, let's assume that the side of the regular pentagon is "x" feet long.
According to the problem, one side of the square is 6 feet longer than a side of the pentagon. Therefore, the side of the square will be (x + 6) feet long.
We know that the square and the pentagon have the same perimeter.
The perimeter of a square is given by the formula: P = 4s, where P is the perimeter and s is the length of a side.
The perimeter of a regular pentagon is given by the formula: P = 5s, where P is the perimeter and s is the length of a side.
Since the perimeters of the square and the pentagon are equal, we can write the equation: 4(x + 6) = 5x.
Simplifying the equation, we get: 4x + 24 = 5x.
Rearranging the equation, we get: 24 = 5x - 4x, which becomes: x = 24.
Therefore, the side length of the regular pentagon is x = 24 feet.
To find the side length of the square, we substitute the value of x back into the equation for the side length of the square: (x + 6).
Substituting x = 24 into (x + 6), we get: 24 + 6 = 30.
Therefore, the side length of the square is 30 feet.
In conclusion, the lengths of the sides of the regular pentagon are 24 feet, and the lengths of the sides of the square are 30 feet.