geomtry word problem need some help

melanie0989

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If in Quadilateral ABCD, side AB is twice side BC, side BC is twice side CD, and side CD is twice side DA, what is the length of side DA if the perimeter of ABCD is 75 in?

I know that the answer is 5in. but I need to know how to get to that point. I know I need to set up one of the sides as x and go from there but not sure which side.
 
If in Quadilateral ABCD, side AB is twice side BC, side BC is twice side CD, and side CD is twice side DA, what is the length of side DA if the perimeter of ABCD is 75 in?
The length of Side AB is given in terms of the length of Side BC; the length of Side BC is given in terms of the length of Side CD; and the length of Side CD is given in terms of the length of Side DA. So pick a variable for the length of Side DA. Then work backwards. ;)
 
If in Quadilateral ABCD, side AB is twice side BC, side BC is twice side CD, and side CD is twice side DA,
what is the length of side DA if the perimeter of ABCD is 75 in?

I know that the answer is 5in. but I need to know how to get to that point. I know I need to set up one
of the sides as x and go from there but not sure which side.

melanie0989,

this problem has no solution. No quadrilateral can have sides with lengths in that ratio.

Suppose I look at a simpler case of sides of 8, 4, 2, and 1. The sum of the lengths of the three sides
other than the side of length 8, as a necessity, must be greater than 8 for it to even be a polygon.

And, in the case of your alleged answer of 5 in. for side DA, that would mean the lengths would be
40 in., 20 in., 10 in., and 5 in. for the perimeter of 75 in.\(\displaystyle \ \ \) In the same way as described
in the above paragraph, the sum of 20 in., 10 in., and 5 in. is not greater than 40 in.

No quadrilateral of perimeter 75 in. with those ratios of side lengths even exists.


You were given a bad problem.
 
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