Question

Each leg of a 45°-45°-90° triangle measures 12 cm. What is the length of the hypotenuse?

Answer 1

Answer:

12 sqrt(2) or 16.97cm

Step-by-step explanation:

h squared = o squared + a squared

so o and a are both 12. you need to find h

h squared = 288

h=12 * square root of 2

Answer 2

Answer:  The length of the hypotenuse is 12√2 units.

Step-by-step explanation:  As shown in the attached figure below, the triangle ABC is a right-angled one, where

m∠B = 90°, m∠A = m∠C = 45°   and   AB = BC = 12 cm.

We are to find the length of the hypotenuse, AC.

From Pythagoras theorem, we have

$AC^2=AB^2+BC^2\\\\\Rightarrow AC=\sqrt{AB^2+BC^2}\\\\\Rightarrow AC=\sqrt{12^2+12^2}\\\\\Rightarrow AC=\sqrt{144+144}\\\\\Rightarrow AC=\sqrt{2\times144}\\\\\Rightarrow AC=12\sqrt2.$

Thus, the length of the hypotenuse is 12√2 units.