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: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\).
In triangle \(QRS\), \(a = 10\) and \(b = 10\) (since both legs are 10 units long).

Step2: Substitute values into the formula

Substitute \(a = 10\) and \(b = 10\) into \(c^{2}=a^{2}+b^{2}\). We get \(c^{2}=10^{2}+10^{2}\).
Calculate \(10^{2}=100\), so \(c^{2}=100 + 100=200\).

Step3: Solve for \(c\)

Take the square root of both sides to find \(c\). \(c=\sqrt{200}\).
Simplify \(\sqrt{200}\): we know that \(200 = 100\times2\), so \(\sqrt{200}=\sqrt{100\times2}=\sqrt{100}\times\sqrt{2}=10\sqrt{2}\).

Answer:

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