Question

using algebra find the value of each variable. write answers in simplest radical form. 14. triangle with legs 2, 2 and hypotenuse e, right - angled

Explanation:

Step1: Apply Pythagorean theorem

The triangle is a right isosceles triangle, so use $a^2 + b^2 = c^2$, where $a=2$, $b=2$, $c=e$.

$$\begin{align*} e^2 &= 2^2 + 2^2 \end{align*}$$

Step2: Calculate the sum of squares

Compute the squared terms and add them.

$$\begin{align*} e^2 &= 4 + 4 = 8 \end{align*}$$

Step3: Solve for $e$

Take the square root and simplify the radical.

$$\begin{align*} e &= \sqrt{8} = 2\sqrt{2} \end{align*}$$

Answer:

$2\sqrt{2}$