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# Math

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what is the length of side c of a right triangle when a and b equal 3 and 4
Mar 18, 2014

#1
+114485
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what is the length of side c of a right triangle when a and b equal 3 and 4

There is not enough information here. you need something else like the angle beteeen the 3 and 4 sides.
Mar 18, 2014
#2
+121056
+8

However........I'm going to change your question slightly to this one:

What could be the length of side c of a right triangle when a and b equal 3 and 4??

Well, by something known as the "triangle inequality," the remaining side is either greater than 1, or less than 7.

Then....either 4 is the longest side (the hypotenuse), or it isn't.

Let's suppose that it is......then, by the Pythagorean Theorem, the remaining side is...... SQRT(4^2 - 3^2) = SQRT(16 - 9) = SQRT(7) ........ which is greater than 1

So, if we're not too picky about whether a side is an integer or not, this could be one solution.

Now, let's suppose that 4 isn't the longest side. Then, again by the "P" Theorem, the remaining side is..... SQRT(3^2 + 4^2) = SQRT(9 + 16) = SQRT(25) = 5.........which is less than 7

So, we have two possible answers.......one right triangle has sides of SQRT(7), 3 and 4, where 4 is the hypotenuse. And the other triangle has sides of 3, 4 and 5, where 5 is the hypotenuse!!

I'm not sure which applies to your particular situation, but exploring possibilities is sometimes more interesting than figuring out "exact" things....

Hope this helps..
Mar 18, 2014
#3
0
the ans is 5 if side c is opposite from the right angle.
Mar 18, 2014
#4
+114485
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Melody:

what is the length of side c of a right triangle when a and b equal 3 and 4

There is not enough information here. you need something else like the angle beteeen the 3 and 4 sides.

I didn't see the word 'right' there before. Sorry.

There are only 2 possible answers
sqrt(3 2+4 4) = sqrt(25) = 5 units
or
sqrt(4 2-3 2) = sqrt(16-9) = sqrt(7) units

Just as Chris and Bob said. :
Mar 18, 2014