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08-29-2005, 03:07 PM
In an isosceles triangle the base is a whole number and is 4 ft. less than the sum of the two equal sides. The perimeter is a whole number between 0 and 75 feet. Find the possible lengths of the equal sides.

What ive got so far is
4x-4=Perimeter
What i dont get is how im sopposed to get the answer with the imformation given.

all help is greatly appreciated.

tkhunny
08-29-2005, 03:31 PM
Rule #1 - Name Stuff - WRITE DOWN clear and concise definitions.

You have a very mysterions formula, 4x - 4 = Perimeter. What is that? Where did it come from? What is 'x'?

Try this:

x = Length of each of the two equal sides of the isosceles triangle.

Now we know what x is and we can proceed. x won't be anything else, as long as we are working on this problem.

2*x - 4 = Length of the third side.

Now add them all up for the perimeter: x + x + 2*x - 4 = 4*x - 4 = Perimeter. Oh, THAT'S where your formula came from!

Good. You got that far.

Your task now it to track down the solution. It isn't always clear how to proceed when being asked for a range of values.

We know this, Perimeter <= 75, leading to 4*x - 4 <= 75, or 4*x <= 79, or x <= 79/4.

We can imagine this, Perimeter > 0, leading to 4*x - 4 > 0, or 4*x > 4, or x > 1. Now we have the possible solutions narrowed down to {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19}

We know the length of the third side is a Whole Number. This makes 2*x - 4 >= 0, or 2*x >= 4, or x >= 2. Well, that didn't help.

That's about it. From the problem statement, there is nothing remaining that we have not utilized. We have a solution set for 'x'. It is very little trouble to calculate the related length of each third side and related perimeter, if you wish to do so, even though the problem statement did not ask for it.