Question

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

Answer 1

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