Question

each leg of a 45°-45°-90° triangle measures 12 cm. what is the length of the hypotenuse?
image of triangle with vertices z, x, y; ∠z = 45°, ∠x = 45°, ∠y = 90°; legs zy = 12 cm, xy = 12 cm
options: 6 cm, 6√2 cm, 12 cm, 12√2 cm

Explanation:

Step1: Recall 45-45-90 triangle ratio

In a \(45^\circ - 45^\circ - 90^\circ\) triangle, the ratio of leg : leg : hypotenuse is \(1:1:\sqrt{2}\). So hypotenuse \(= \text{leg} \times \sqrt{2}\).

Step2: Substitute leg length

Given leg length is \(12\) cm. So hypotenuse \(= 12 \times \sqrt{2} = 12\sqrt{2}\) cm.

Answer:

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