Question

one leg of an isosceles right triangle measures 5 inches. rounded to the nearest tenth, what is the approximate length of the hypotenuse?
2.5 inches
5.0 inches
7.1 inches
9.8 inches

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \( c = \sqrt{a^2 + b^2} \). In an isosceles right triangle, \( a = b = 5 \) inches.

Step2: Substitute values into formula

\( c = \sqrt{5^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50} \)

Step3: Calculate and round

\( \sqrt{50} \approx 7.071 \), rounded to the nearest tenth is \( 7.1 \).

Answer:

7.1 inches (corresponding to the option: 7.1 inches)