Question

8-1: practice & problem-solving day 1
find the value of x. if necessary, write your answer in simplest radical form.
$x=\square$
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse. Here, $a=6$, $b=7$, $c=x$.
$$6^2 + 7^2 = x^2$$

Step2: Calculate squared terms

Compute the squares of the legs.
$$36 + 49 = x^2$$

Step3: Sum and solve for x

Add the values, then take the positive square root (side length is positive).
$$85 = x^2 \implies x = \sqrt{85}$$

Answer:

$\sqrt{85}$