Question

consider triangle qrs. the legs each have a length of 10 units. what is the length of the hypotenuse of the triangle? 5 units 5√2 units 10 units 10√2 units

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(a = 10\), \(b = 10\), and \(c\) is the hypotenuse.
$$10^{2}+10^{2}=c^{2}$$

Step2: Simplify the equation

Calculate \(10^{2}+10^{2}\):
$$100 + 100=c^{2}$$
$$200=c^{2}$$

Step3: Solve for \(c\)

Take the square root of both sides:
$$c=\sqrt{200}$$
Simplify \(\sqrt{200}=\sqrt{100\times2}=10\sqrt{2}\)

Answer:

\(10\sqrt{2}\) units (the fourth option)