Question

solve for m in the provided triangle. note that the diagram may not be to scale.
options: m = √75, m = 9, m = √125, m = 75

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here, if the hypotenuse is 10 and the two legs are 5 and \(m\), then \(10^{2}=5^{2}+m^{2}\).

Step2: Rearrange the equation to solve for \(m^{2}\)

\(m^{2}=10^{2}-5^{2}\). Calculate \(10^{2}=100\) and \(5^{2}=25\), so \(m^{2}=100 - 25=75\).

Step3: Solve for \(m\)

Take the square root of both sides. Since \(m>0\) (as it represents the length of a side of a triangle), \(m = \sqrt{75}\).

Answer:

\(m=\sqrt{75}\)