Question

find v.
write your answer in simplest radical form.
meters

Explanation:

Step1: Identify triangle type

This is a right isosceles triangle (two 45° angles, right angle), so the two legs are equal, let each leg length be $x$. The hypotenuse is $5\sqrt{2}$ m.

Step2: Apply Pythagorean theorem

For a right triangle, $x^2 + x^2 = (\text{hypotenuse})^2$
$$2x^2 = (5\sqrt{2})^2$$

Step3: Calculate right-hand side

$$(5\sqrt{2})^2 = 5^2 \times (\sqrt{2})^2 = 25 \times 2 = 50$$
So $2x^2 = 50$

Step4: Solve for $x^2$

$$x^2 = \frac{50}{2} = 25$$

Step5: Solve for $x$

$$x = \sqrt{25} = 5$$
Since $v$ is a leg of the triangle, $v = x$.

Answer:

5 meters