Question

each leg of a 45° - 45° - 90° triangle measures 14 cm. what is the length of the hypotenuse? 7 cm 7√2 cm 14 cm 14√2 cm

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 14\), \(b = 14\), and \(c\) is the hypotenuse.
Substitute \(a\) and \(b\) into the formula: \(c^{2}=14^{2}+14^{2}\).

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

\(c^{2}=196 + 196=392\).

Step3: Solve for \(c\)

\(c=\sqrt{392}=\sqrt{196\times2}=14\sqrt{2}\).

Answer:

\(14\sqrt{2}\text{ cm}\) (the fourth option)