Question

select the correct answer.
what is the value of x in the triangle?
triangle image with legs 10, 10 and hypotenuse x
a. (10sqrt{2})
b. (10)
c. (20)
d. (20sqrt{2})
e. (10sqrt{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. $10\sqrt{2}$