Question

what is the length of the hypotenuse of the triangle below? a. 10 b. 10\sqrt{2} c. 25\sqrt{2} d. 5\sqrt{2} e. 1 f. 5

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs of the right - triangle and \(c\) is the hypotenuse. Here \(a = 5\sqrt{2}\) and \(b = 5\sqrt{2}\).

Step2: Substitute values into the formula

\(c^{2}=(5\sqrt{2})^{2}+(5\sqrt{2})^{2}\). First, \((5\sqrt{2})^{2}=5^{2}\times(\sqrt{2})^{2}=25\times2 = 50\). So \(c^{2}=50 + 50=100\).

Step3: Solve for \(c\)

Take the square root of both sides. Since \(c>0\) (as it represents the length of a side of a triangle), \(c=\sqrt{100}=10\).

Answer:

A. 10