Find the value of x. if your answer is not an integer, leave it in simplest radical form. the diagram is not drawn to scale.

x = 5sqrt(3)

Step-by-step explanation:

This is a right triangle.  We can use the Pythagorean theorem to solve

a^2 +b^2 = c^2

5^2 +x^2 = 10^2

25+x^2 = 100

Subtract 25 from each side

25-25 +x^2 = 100-25

x^2 = 75

Take the square root of each side

sqrt(x^2) = sqrt(75)

x = sqrt(3*25)

Remember sqrt(ab) = sqrt(a)sqrt(b)

x = sqrt(5)sqrt(3)

x = 5sqrt(3)

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.