Question 200264
a^2+b^2=c^2 is the formula for a right triangle given the three sides.
x^2+(2x+2)^2=(2x+3)^2
x^2+4x^2+8x+4=4x^2+12x+9
x^2+8x-12x+4-9=0
x^2-4x-5=0
(x-5)(x+1)=0
x-5=0
x=5 ft. ans. for the shorter leg. 
2*5+2=10+2=12 ft. ans. for the longer leg.
2*5+3=10+3=13 ft. ans. for the hypotenuse.
Proof:
5^2+12^2=13^2
25+144=169
169=169