When [tex]x=1[/tex] the perimeters of both figures will be equal.
Step-by-step explanation:
Step 1:
The triangle has side lengths of [tex]x+1, x+4,[/tex] and [tex]x+4[/tex].
The perimeter of the triangle is the sum of the lengths of the sides.
The perimeter of the triangle [tex]= x+1+x+4+x+4 = 3x + 9.[/tex]
Step 2:
The perimeter of the hexagon is 6 times its side length. The side length [tex]=2x.[/tex]
The perimeter of the hexagon[tex]= 6(2x) = 12x.[/tex]
Step 3:
To determine the value at which both the perimeters are equal, we equate both the equations to each other.
[tex]3x+9 = 12x, 9 = 9x, x =1.[/tex]
So when [tex]x=1[/tex] the perimeters of both figures will be equal.
