#### Answer

x=5
(2x+3) = 13
(2x+2)= 12

#### Work Step by Step

By Pythagoras Theorem
$(2x+3)^{2} = (2x+2)^{2} +x^{2}$
$4x^{2}+9+12x = 4x^{2} +4+8x+x^{2}$
$x^{2} -4x-5 = 0$
$x^{2} -(5-1)x-5 = 0$
$x^{2} -5x+x-5 = 0$
$x(x-5)+1(x-5) $
$(x-5)(x+1)=0$
x=5 that is correct
x=-1 that is not possible because length can not be negative
(2x+3) = 13
(2x+2)= 12