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 right triangle $QRS$, hypotenuse $c$ satisfies $c^2 = a^2 + b^2$, where $a=10$, $b=10$.
$c^2 = 10^2 + 10^2$

Step2: Calculate sum of squares

$c^2 = 100 + 100 = 200$

Step3: Solve for hypotenuse

Take square root of both sides:
$c = \sqrt{200} = \sqrt{100 \times 2} = 10\sqrt{2}$

Answer:

D. $10\sqrt{2}$ units