I need to find the length x as if it was a triangle, then express the answer in simlified radical form:?

Question

Each numbe represents a side of the triangle:

12

8

x

Answer 1

You really don't give us enough information here. If all you know is that "x" is a side of a triangle, the most you could say is that it's between 4 and 20 (by a rule called the Triangle Inequality which says any two sides must add up to more than the third side).

Most likely you mean it's a side of a RIGHT triangle, but even then you don't say WHICH side. If it's the hypotenuse, you'd have x = SQR(12^2+8^2) = SQR(144+64) = SQR(208).

If x is a leg (one of the shorters sides), you'd hae x = SQR(12^2-8^2) = SQR(80).

Either way, you need to simplify the root. To do this, you need to find perfect squares that go into the numbers.

SQR(208) = SQR(16)*SQR(13) = 4*SQR(13). You'd normally write this as 4 radical 13.

SQR(80) = SQR(16)*SQR(5) = 4*SQR(5). You'd normally write this as 4 radical 5.

You'll need to check what the problem actually says, but your answer should be here.

Answer 2

Is this a right angle triangle? If it is, You need to use Pythagorean Theorem. A(squared)+B(squared)=C(squared)

So you need to know which side is the longest side, which is the one that is NOT part of the right angle that is the C part of the triangle. Just work from there, for example, if the X is the C side, then it would go as follows:

8(squared)+12(squared)=X(squared)
64+144=X(squared)
208=X(squared)
Square root of 208 = square root of X(squared)
14.42 = X

Don't know if this is what you were looking for, Good Luck!