Answer:
x = ⅗ = 0.6
Step-by-step explanation:
A square has four equal sides.
If a square has a side length of [tex] x + 3 [/tex], therefore,
Perimeter of the square = [tex] 4(x + 3) [/tex]
[tex] = 4x + 12 [/tex].
Also, a regular octagon has 8 equal sides.
If it has a side length of 3x, therefore:
Perimeter of the octagon = [tex] 8(3x) [/tex]
= [tex] 24x [/tex]
Given that the Perimeter of the rectangle and the octagon are the same, to find the value of x, set each perimeter equal to the other.
Thus:
[tex] 24x = 4x + 12 [/tex]
Subtract 4x from each side
[tex] 24x - 4x = 12 [/tex]
[tex] 20x = 12 [/tex]
Divide both sides by 20
x = 12/20 = ⅗ = 0.6.
