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

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

 

Will use Pythagoras's Theorem:

 

(3x)^2 + 15^2=(3x + 3)^2

Solve for x:
9 x^2+225 = (3 x+3)^2

Expand out terms of the right hand side:
9 x^2+225 = 9 x^2+18 x+9

Subtract 9 x^2+18 x+9 from both sides:
216-18 x = 0

Factor constant terms from the left hand side:
-18 (x-12) = 0

Divide both sides by -18:
x-12 = 0

Add 12 to both sides:
Answer: | x = 12