Answer:
x=4.5 inches
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The perimeter of a hexagon is the sum of its six length sides
Let
x ----> the length of a shorter side
y ---> the length of a longer side
The perimeter of the hexagon is equal to
[tex]P=4x+2y[/tex]
[tex]P=52\ in[/tex]
so
[tex]52=4x+2y[/tex] ---->equation A
Each longer side measure 1 in. less than 4 times the length of a shorter side
so
[tex]y=4x-1[/tex] ----> equation B
substitute equation B in equation A
[tex]52=4x+2(4x-1)[/tex]
Solve for x
[tex]4x+8x=52+2\\12x=54\\x=4.5\ in[/tex]
