Question

Two squares have sides x cm and (x+4)cm.The sun of their area is 356cm find the value of x

Answer 1

`\huge\boxed{x=√(174)-2}`

Explanation:

`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√(174)\qquad|\text{subtract 2 from both sides}\\\\x=√(174)-2\ \vee\ x=-√(174)-2<0`