Question

what is the length of the hypotenuse in the triangle?

Explanation:

Step1: Identify the type of triangle

Assume it's a right - angled isosceles triangle (since no other angle information is given and we need to use a common right - triangle property). Let the length of each of the two equal sides be \(a = 14\) cm.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the other two sides. In an isosceles right - triangle \(a = b\). So \(c^{2}=14^{2}+14^{2}=196 + 196=392\). Then \(c=\sqrt{392}=\sqrt{196\times2}=14\sqrt{2}\) cm.

Answer:

\(14\sqrt{2}\text{ cm}\)