Question

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

Answer 1

12 sqrt(2) or 16.97cm

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=√(AB^2+BC^2)\\\\\Rightarrow AC=√(12^2+12^2)\\\\\Rightarrow AC=√(144+144)\\\\\Rightarrow AC=√(2*144)\\\\\Rightarrow AC=12\sqrt2.`

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