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