The two figures below, a regular hexagon and a regular pentagon, have the same perimeter. What is the length of a side of the pentagon?

69

Step-by-step explanation:

Perimeter = sum of all sides of a regular polygon = the number of sides*length of a side

Length of a side of the given regular hexagon = 3x + 5

Perimeter of hexagon = 6(3x + 5) = 6(3x) + 6(5) = 18x + 30

Length of a side of the given regular pentagon = 4x - 1

Perimeter of pentagon = 5(4x - 1) = 5(4x) - 5(1) = 20x - 5

Since we are told that the perimeter of the regular hexagon is the same as that of the regular pentagon, therefore:

18x + 30 = 20x - 5

Solve for x.

Subtract 20x from both sides

18x + 30 - 20x = 20x - 5 - 20x

-2x + 30 = -5

Subtract 30 from both sides

-2x+ 30 - 30 = -5 - 30

-2x = -35

Divide both sides by -2

x = -35/-2

x = 17.5

Length of a side of pentagon = 4x - 1

Plug in the value of x

4(17.5) - 1 = 70 - 1 = 69

length of a side of the pentagon = 69

step-by-step explanation:

use pothagarean therom

a^2+b^2=c^2 so first ac

acm is a right triangle because c= 90°

and am (the hypotenuse or c) =16+9 =25

but there is not enough info we need another angle or side length