Question

The perimeter of this hexagon is 52in. Each longer side measure 1 in. less than 4 times the length of a shorter side. Find the length of the labeled x.

Answer 1

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

$P=4x+2y$

$P=52\ in$

so

$52=4x+2y$ ---->equation A

Each longer side measure 1 in. less than 4 times the length of a shorter side

so

$y=4x-1$ ----> equation B

substitute equation B in equation A

$52=4x+2(4x-1)$

Solve for x

$4x+8x=52+2\\12x=54\\x=4.5\ in$