Question

step 1: \frac{short}{long}=\frac{short}{long}

Explanation:

Step1: Apply Pythagorean theorem

For the first right - angled triangle with legs of length \(1.5\) (since the side of length \(3\) is divided equally) and \(1.5\), by \(a^{2}+b^{2}=c^{2}\), we have \(x_{1}=\sqrt{1.5^{2}+1.5^{2}}=\sqrt{2\times1.5^{2}}=\frac{3\sqrt{2}}{2}\).
For the second right - angled triangle with legs of length \(\sqrt{7}/2\) and \(\sqrt{7}/2\), by \(a^{2}+b^{2}=c^{2}\), we have \(x_{2}=\sqrt{(\frac{\sqrt{7}}{2})^{2}+(\frac{\sqrt{7}}{2})^{2}}=\sqrt{\frac{7}{4}+\frac{7}{4}}=\frac{\sqrt{14}}{2}\).

Answer:

For the first triangle \(x = \frac{3\sqrt{2}}{2}\), for the second triangle \(x=\frac{\sqrt{14}}{2}\)