If one side of an isosceles triangle has length 1002 and another side has length 2004, what is the perimeter?

Question

What is the perimeter of the triangle?

Answer 1

This is not a problem about two separate triangles, in fact, only one is possible. If the third side of the isosceles triangle were 1002, you would not have a triangle at all, but two lines laying on top of the third. The only solution is that the third side must equal 2004. Therefore, since perimeter (for short, we'll call this P) is the distance traced around a given shape, we have the following:

P = a + b + c (where a,b,c are sides of the given triangle)

P = 1002 + 2004 + 2004

P = 5010

And there you have it!

Answer 2

the perimeter of a triangle is the sum of the lengths of the sides.

isosceles triangles have 2 equal sides.

the perimeter is then either 4008 or 5010.

there are two answers.  you never make assumptions in math.

Answer 3

An isosceles triangle has two equal sides and one smaller side. the equal sides are usually the longest so assume the equal sides are 2004.

therefore the perimeter is 2 x 2004 + 1002 = 5010

Answer 4

There are two answers to this.

But remember that an isosceles triangle has two sides of equal length.

If you take the side of length 1002 to be for two sides of the triangle, than the solution will be:    (1002*2)+2004  which gives you an answer of 4008.

But if you take the side of length 2004 to be for two sides of the triangle, than the solution will be:   (2004*2)+1002  which gives you an answer of 5010.

Answer:    

4008  (L=1002)            or            

5010  (L=2004)

Answer 5

Sorry, troops, Michael S is correct.  One quick check for whether a triangle is possible given the lengths of three segments is that for every possible pair, the sum of the sides in the pair must be greater than the length of the remaining side.  A triangle can have sides of length 3, 4, and 5 because 3+4>5, 3+5> 4, and 4+5>3.

Applying this to the question, and knowing that an isosceles triangle has at least two equal sides (an equilateral triangle is a special case of isosceles triangle, but that does not affect this question), the possible lengths for the sides of this triangle are (1002, 1002, 2004) and (1002, 2004, 2004) .  Since 1002+1002 is not greater than 2004, the first set of sides is not possible.  As Michael S pointed out, this would give you two "sides" laying on top of the base, or a line on top of a line.  1002+2004>2004 and 2004+2004>1002, so the sides must be 1002, 2004, and 2004, making the perimeter 5010.

Answer 6

An isoceles triangle means that 2 sides have the same length and one side is different from the two.

So,

Perimeter = 2004 + 2004 + 1002 = 5010.

The longer side will be 2004 (which are the 2 sides)

Think about this:

Remember the hypothenus? That is the longest side of the triangle.

An isoceles triangle has 2 sides (hypothenus).

Something like this:

http://img502.imageshack.us/my.php?image...

Can you see that the 2 sides are longer than the other?

Answer 7

In an isosceles triangle, two sides are of equal length,

so considering your given S1 = 2004, and S2 = 1002, since there is no probability that the other side is 1002, S3 will always be 2004 no matter what (1002 + 1002 will be 2004, and if this happens, it is just a straight line, and not a triangle,  so this one is eliminated), then the perimeter will be S1 + S2 + S3

P = 1002 + 2004 + 2004 = 5010.

P = 5010