Question

find x and leave answers in simplest radical form

Explanation:

Step1: Apply Pythagorean theorem for first triangle

For a right - angled triangle with legs \(a = 3\), \(b = 3\) and hypotenuse \(x\). By Pythagorean theorem \(a^{2}+b^{2}=x^{2}\). So \(3^{2}+3^{2}=x^{2}\), \(9 + 9=x^{2}\), \(x^{2}=18\), \(x=\sqrt{18}=3\sqrt{2}\)

Step2: Apply Pythagorean theorem for second triangle

For a right - angled triangle with legs \(a = 7\), \(b = 7\sqrt{3}\) and hypotenuse \(x\). By Pythagorean theorem \(a^{2}+b^{2}=x^{2}\). So \(7^{2}+(7\sqrt{3})^{2}=x^{2}\), \(49+147=x^{2}\), \(x^{2}=196\), \(x = 14\)

Answer:

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