Each leg of a $45°-45°-90°$ triangle measures $14\mathrm{cm}$. What is the length of the hypotenuse?

• A. $14÷\sqrt{2}\approx 9.9\mathrm{cm}$
• B. $14\mathrm{cm}$
• C. $14\times \sqrt{2}=14\sqrt{2}\approx 19.8\mathrm{cm}$
• D. $14\times 2=28\mathrm{cm}$

Answer: (C)

Verified step by step guidance

1. Recognize that the triangle is a 45°-45°-90° right triangle, which is an isosceles right triangle where the legs are congruent.
2. Recall the special property of a 45°-45°-90° triangle: the hypotenuse length is equal to the leg length multiplied by \( \sqrt{2} \). This comes from the Pythagorean theorem applied to the legs of equal length.
3. Identify the given leg length as 14 cm. Let the hypotenuse be denoted as \( h \). According to the property, write the equation: \( h = 14 \times \sqrt{2} \).
4. Set up the expression for the hypotenuse length without calculating the decimal value: \( h = 14 \times \sqrt{2} \).
5. If needed, you can approximate \( \sqrt{2} \approx 1.414 \) to find a decimal approximation for the hypotenuse, but the exact form is preferred for precision.