SOLUTION: I am stumped on this question and I am not sure how to figure out the perimeter. If I knew that number I could solve the problem. Thanks for your help. Consider a square and a r

Question 263346: I am stumped on this question and I am not sure how to figure out the perimeter. If I knew that number I could solve the problem. Thanks for your help.
Consider a square and a regular hexagon (a six sided figure with sides of equal length). One side of the square is 7 feet longer than a side of the hexagon, and the two figures have the same perimeter. What are the lengths of the sides of each figure?
I set it up as x= hexagon
x+7= square
x+x+7=?
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
The trick is to find the sides then find the perimeter not the perimeter first.
We know that
the side nof the square is 7 more than the side of the hexagon
s=h+7 and
and we know that the perimeter of the square is 4s
and the hexagon is 6h
and the the two perimeters are equal
4s=6h
s=h+7
substitute h+7 for s
4(h+7)=6h
4h+28=6h
28=2h
14=h
s=h+7
s=21
h=14 s=21
check
6*14=4*21
84=84
both perimeters equal 84
ok
This problem should be in the word problem geometry category
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Consider a square and a regular hexagon (a six sided figure with sides of equal length).
One side of the square is 7 feet longer than a side of the hexagon, and the two figures have the same perimeter.
What are the lengths of the sides of each figure?
---------------
Let a side of the square be "x".
Perimeter of the square = 4x
------------------
A side of the hexagon is x-7
Perimeter of the hexagon is 6(x-7) = 6x-42
----------------
Equation:
Sq. P = Hex P
4x = 6x-42
2x = 42
x = 21
---
P of the Sq = 4x = 84
P of the Hex = 6*14 = 84
==============================
Cheers,
Stan H.
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