Question

select the correct answer.
what is the value of x in the triangle?
a. $10\sqrt{2}$
b. 10
c. 20
d. $20\sqrt{2}$
e. $10\sqrt{3}$

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $a=10$, $b=10$, $c=x$.

Step2: Substitute values into formula

$10^2 + 10^2 = x^2$

Step3: Calculate left-hand side

$100 + 100 = x^2$
$200 = x^2$

Step4: Solve for x

$x = \sqrt{200} = \sqrt{100 \times 2} = 10\sqrt{2}$

Answer:

A. $10\sqrt{2}$