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A regular hexagon and a rectangle have the same perimeter, P. A side of the hexagon is 4 less than the length, l, of the rectangle. The width of the rectangle, w, is 2 less than the length of the rectangle. What is the perimeter of the hexagon?

Respuesta :

calculista

Answer:

The perimeter of the hexagon is equal to [tex]36\ units[/tex]

Step-by-step explanation:

Let

x-------> the length side of the hexagon

L-----> the length of the rectangle

W-----> the width of the rectangle

we know that

The perimeter of the hexagon is equal to

[tex]P=6x[/tex]

The perimeter of the rectangle is equal to

[tex]P=2L+2W[/tex]

so

[tex]6x=2L+2W[/tex]

[tex]3x=L+W[/tex] -------> equation A

[tex]x=L-4[/tex] -------> equation B

[tex]W=L-2[/tex] -------> equation C

Substitute equation B and equation C in equation A

[tex]3[L-4]=L+[L-2][/tex]

Solve for L

[tex]3L-12=2L-2[/tex]

[tex]3L-2L=12-2[/tex]

[tex]L=10\ units[/tex]

Find the value of x

[tex]x=L-4[/tex]

[tex]x=10-4=6\ units[/tex]

Find the perimeter of hexagon

[tex]P=6x[/tex]

[tex]P=6(6)=36\ units[/tex]

Answer:

36

Step-by-step explanation:

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