Answer:
[tex]\huge\boxed{x=\sqrt{174}-2}[/tex]
Step-by-step explanation:
[tex]A_1=x^2cm^2\\\\A_2=(x+4)^2cm^2\\\\A_1+A_2=356\\\\x^2+(x+4)^2=356\qquad|\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\x^2+x^2+8x+16=356\qquad|\text{subtract 16 from both sides}\\\\2x^2+8x=340\qquad|\text{divide both sides by 2}\\\\x^2+2\cdot x\cdot2=170\qquad|\text{add}\ 2^2\ \text{to both sides}\\\\x^2+2\cdot x\cdot 2+2^2=174\qquad|\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2=174\to x+2=\pm\sqrt{174}\qquad|\text{subtract 2 from both sides}\\\\x=\sqrt{174}-2\ \vee\ x=-\sqrt{174}-2<0[/tex]
