Question

consider triangle qrs. the legs each have a length of 10 units.
what is the length of the hypotenuse of the triangle?
options: 10 units, 5√2 units, 5 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 \(c^{2}=a^{2}+b^{2}\).
Here, \(a = 10\) units and \(b = 10\) units.

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: \(c=\sqrt{200}\).
Simplify \(\sqrt{200}=\sqrt{100\times2}=10\sqrt{2}\) (since \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) for \(a = 100\), \(b = 2\) and \(\sqrt{100}=10\)).

Answer:

\(10\sqrt{2}\) units