1. ## Pythagorean thrm and radicals help

Hello. I know the answers to these problems but I'm not quite sure how to arrive at them.

Basically I just have to find x.

1. A rt triangle with hypotenuse 2x, and legs x and 5 radical 3 (the 3s under the radical). The equation should be xsquared + (5 radical 3) squared = 2xsquared and the answer is x = 5.

2. A rect has length 2.4 and width 1.8. I have to find the diagonal. I set the equation up as xsquared = 2.4squared + 1.8squared. The answer is 3.

What I would like is if someone could show the exact steps for arriving at the answer (all the little details as well if possible) as I can't quite seem to work them out correctly. Thanks.

2. Originally Posted by Phil
Hello. I know the answers to these problems but I'm not quite sure how to arrive at them.

Basically I just have to find x.

1. A rt triangle with hypotenuse 2x, and legs x and 5 radical 3 (the 3s under the radical). The equation should be xsquared + (5 radical 3) squared = 2xsquared and the answer is x = 5.

2. A rect has length 2.4 and width 1.8. I have to find the diagonal. I set the equation up as xsquared = 2.4squared + 1.8squared. The answer is 3.

What I would like is if someone could show the exact steps for arriving at the answer (all the little details as well if possible) as I can't quite seem to work them out correctly. Thanks.
Just the first one, and hopefully you can see how it applies to the second. Use Pythagorean theorem to write equation. Then it is just algebraic manipulation.

$x^2+(5\sqrt{3})^2=(2x)^2$

$x^2+25\cdot3=4x^2$

$3x^2=25\cdot3$

$x^2=25$

$x=\pm5$

Cast out the negative answer because side length is positive

$x=5$

3. Okay, I see now what I did wrong now. And it seems I must have just added the numbers in the second one wrong because I'm finally got 3.

Anyways, thanks for the help.