Answer:
x= 18cm
Step-by-step explanation:
Applying pythagoras' rule
(x)²+(x+6)²=(x+12)²
Open the brackets
x²+x²+12x+36=x²+24x+144
Collect like terms to the LHS
x²+x²-x²+12x-24x+36-144=0
x²-12x-108=0
Solving the quadratic equation
a=1,b= - 24,c= - 108,ac= - 108
Factors are - 18 & +6
x²-18x+6x-108=0
(x²-18x)+(6x-108)=0
x(x-18)+6(x-18)=0
(x-18)(x+6)=0
x-18=0 or x+6=0
x=0+18 or x=0-6
x=18 or x= - 6
In cases like this it's the positive answers that are chosen
Therefore, x=18cm
