Question

what is the length of leg s of the triangle below? a. $sqrt{6}$ b. $sqrt{72}$ c. 36 d. 3 e. 3.2 f. 6

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, if one leg is \(6\) and the other is \(s\), and the hypotenuse \(c = \sqrt{72}\), then \(6^{2}+s^{2}=(\sqrt{72})^{2}\).

Step2: Simplify the equation

We know that \(6^{2}=36\) and \((\sqrt{72})^{2}=72\). So the equation becomes \(36 + s^{2}=72\).

Step3: Solve for \(s^{2}\)

Subtract 36 from both sides of the equation: \(s^{2}=72 - 36\), so \(s^{2}=36\).

Step4: Solve for \(s\)

Take the square - root of both sides. Since \(s\) represents the length of a side of a triangle, we take the positive square root. So \(s=\sqrt{36}=6\).

Answer:

F. 6