SOLUTION: The larger leg of a right triangle is 3 centimeters longer than its smaller leg. The hypotenuse is 6 centimeters longer than the smaller leg. How many centimeters long is the small

Algebra ->  Pythagorean-theorem -> SOLUTION: The larger leg of a right triangle is 3 centimeters longer than its smaller leg. The hypotenuse is 6 centimeters longer than the smaller leg. How many centimeters long is the small      Log On


   

Question 754382: The larger leg of a right triangle is 3 centimeters longer than its smaller leg. The hypotenuse is 6 centimeters longer than the smaller leg. How many centimeters long is the smaller leg?
Found 2 solutions by Cromlix, dkppathak:
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Using Pythagoras
Hypotenuse = (x + 6)
Longer leg = (x + 3)
Short leg = x
Therefore x^2 + (x + 3)^2 = (x + 6)^2
x^2 + (x^2 + 6x + 9) = (x^2 + 12x + 36)
2x^2 + 6x + 9 = x^2 + 12x + 36
2x^2 - x^2 + 6x - 12x + 9 - 36 + 0
x^2 - 6x - 27 = 0
(x + 3)(x - 9)+ 0
Therefore x = -3 (No answer)
x = 9
Short leg = 9cm
Hypotenuse^2 = Longer leg^2 + short leg^2
(9 + 6)^2 = (9 + 3)^2 + 9^2
15^2 = 12^2 + 9^2
225 = 144 + 81
225 = 225 Proved
Hope this helps
:-)

Answer by dkppathak(439) About Me  (Show Source):
You can put this solution on YOUR website!
let smaller leg is x
other leg is x+3
and hypotenuse is x+6
using Pythagoras theorem
(x+6)^2=x^2+(x+3)^2
x^2+36+12x=x^2+X^2+9+6x
x^2-6x-27=0
x^2-9x+3x-27=0
(x-9)(x+3)=0
x=9 or x=-3
so side are 9 12 and 15 cm
ANSWER 9 12 15 cm