Question

each leg of a 45°-45°-90° triangle measures 12 cm. what is the length of the hypotenuse? triangle diagram with right angle at y, legs yz and yx both 12 cm, angles at z and x both 45° multiple choice options: 6 cm, 12 cm, $6sqrt{2}$ cm, $12sqrt{2}$ cm

Explanation:

Step1: Recall 45-45-90 triangle ratio

In a 45-45-90 triangle, the legs are equal, and the hypotenuse \( h \) is related to a leg \( l \) by \( h = l\sqrt{2} \).

Step2: Substitute the leg length

Given each leg \( l = 12 \) cm, so hypotenuse \( h = 12\sqrt{2} \) cm.

Answer:

\( 12\sqrt{2} \) cm (corresponding to the option with \( 12\sqrt{2} \) cm text)