SOLUTION: one leg of a right triangle is 3 millimeters shorter than the longer leg and the hypotenuse is 3 millimeters longer than the longer leg. find the lengths of the sides of the triang

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Question 823899: one leg of a right triangle is 3 millimeters shorter than the longer leg and the hypotenuse is 3 millimeters longer than the longer leg. find the lengths of the sides of the triangle.
The length of the longer leg is? millimeters
The length of the shorter leg is? millimeters
The length of the hypotenuse is? millimeters
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
let legs be a and b, and the hypotenuse c
let shorter leg be a=x
then the longer leg is b=a%2B3 or b=x%2B3
if the hypotenuse c is 3 millimeters longer than the longer leg b, then c=b%2B3.....substitute b=x%2B3 and you have c=x%2B3%2B3=x%2B6
use Pythagorean theorem:
c%5E2=a%5E2%2Bb%5E2
%28x%2B6%29%5E2=x%5E2%2B%28x%2B3%29%5E2................solve for x
x%5E2%2B12x%2B36=x%5E2%2Bx%5E2%2B6x%2B9
x%5E2%2B12x%2B36=2x%5E2%2B6x%2B9
0=2x%5E2%2B6x%2B9-x%5E2-12x-36
x%5E2-6x-27=0............write -6x as -9x%2B3x
x%5E2-9x%2B3x-27=0............group
%28x%5E2-9x%29%2B%283x-27%29=0............factor out x and 3
x%28x-9%29%2B3%28x-9%29=0

%28x%2B3%29%28x-9%29=0
solutions:
if %28x%2B3%29=0 => x=-3...........leg cannot be negative length, so disregard this solution
if %28x-9%29=0=> x=9..............your solution; now use it to find out the length of legs and hypotenuse
a=x=>a=9
b=x%2B3 =>b=9%2B3 =>b=12
c=x%2B6=>c=9%2B6=>c=15

check our solution:
c%5E2=a%5E2%2Bb%5E2
15%5E2=9%5E2%2B12%5E2
225=81%2B144
225=225