Question

consider triangle qrs. the legs each have a length of 10 units. image of right triangle qrs with right angle at s, qs=10, sr=10 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, \( c = \sqrt{a^2 + b^2} \), where \( a,b \) are legs, \( c \) is hypotenuse.
Here, \( a = 10 \), \( b = 10 \).

Step2: Substitute values into formula

\( c = \sqrt{10^2 + 10^2} = \sqrt{100 + 100} = \sqrt{200} \)

Step3: Simplify the square root

\( \sqrt{200} = \sqrt{100 \times 2} = 10\sqrt{2} \)

Answer:

\( 10\sqrt{2} \) units (corresponding to the option "10√2 units")