The legs of a right triangle measure 3x and 15. If the hypotenuse measures 3x + 3, what is the value of x?

a. 221

b. 12

c. 36

d. 16

The answer is b. 12

According to the Pythagorean theorem the square of the hypotenuse (c) is the sum of the squares of the legs (a and b):

c² = a² + b²

We have:

a = 3x

b = 15

c = 3x + 3

Now, let's replace these parameters:

c² = a² + b²

(3x + 3) ² = (3x) ² + 15²

(3x) ² + 2 * 3x * 3 + 3² = 9x² + 225

9x² + 18x + 9 = 9x² + 225

Rearrange:

9x² - 9x² + 18x = 225 - 9

18x = 216

x = 216 / 18 = 12