Question

Solve for x using Pythagorean theorem

Answer 1

From the Pythagorean theorem, we have

$(2x)^2 + (3x)^2 = (\sqrt{52})^2$

Simplifying both sides gives

$4x^2 + 9x^2 = 52 \\\\ 13x^2 = 52 \\\\ x^2 = \dfrac{52}{13} = 4 \\\\ x = \pm\sqrt4 = \pm2$

But we're talking about lengths, which can't be negative, so x = 2.