Get length and width of a television

Question

TV measures $12$ inches diagonally, and the length is $2\times$ more than the width. What are the dimensions of the TV.

I thought:

$a = \text{width}$
$b = \text{height}$
$c = \text{diagonal}$

$c = 12$
$a = x$
$b = x+2$

so

$x^2 + (x+2)^2 = 12^{12}$

then solve for $x$.

But when I do, the answer is completely wrong.

Answer 1

When you say "the length is 2x more than the width", does that mean the length is three times the width or twice? If it is three times, your $b=x+2$ should be replaced by $b=3x$. If it is twice, it should be $b=2x$. At the end of the last equation it should be $12^2$, not $12^{12}$

Answer 2

Pythagorean theorem implies that $\text{length}^2+\text{width}^2=\text{diagonal}^2$. The length is twice the width so the equation should be $$x^2 + (2x)^2 = 12^{2}\iff 5x^2= 12^{2}$$ which you can solve for $x$, noting that $x>0$.