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: Apply Pythagorean theorem

In an isosceles right - triangle, the two legs \(a = b=5\) inches. By the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse. Substitute \(a = 5\) and \(b = 5\) into the formula: \(c^{2}=5^{2}+5^{2}\).

Step2: Calculate \(c^{2}\)

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

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{50}\). Simplify \(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\approx5\times1.414 = 7.07\).

Step4: Round to the nearest tenth

Rounding \(7.07\) to the nearest tenth gives \(7.1\).

Answer:

C. 7.1 inches