Question

Each leg of a 45°-45°-90° triangle measures 14 cm. What is the length of the hypotenuse?● 7cm●
`7 √(2)`●14cm
`14 √(2cm)`

Answer 1

Step-by-step explanation

If we have a 45°- 45°- 90° triangle, two or the sides have the same length and the hypotenuse can be calculated using the Pythagorean Theorem as:

`\text{Hypotenuse}=\sqrt[]{x^2+x^2}`

Where x is the length of the sides. So, replacing x by 14, we get:

`\begin{gathered} \text{Hypotenuse}=\sqrt[]{14^2+14^2} \\ \text{Hypotenuse}=\sqrt[]{2(196^{})} \\ \text{Hypotenuse}=\sqrt[]{196}\cdot\sqrt[]{2} \\ \text{Hypotenuse}=14\sqrt[]{2} \end{gathered}`

Therefore, the answer is: 14√2

Answer: 14√2