Question

The side of one square is 2 centimeters longer than the side of the second square. If the sun of their areas is 100cm2, find the length of the side of each square.

Answer 1

`x,\ x+2-length\ of\ sides\ of\ the\ squares\\\\x^2,\ (x+2)^2-the\ areas\ of\ the\ squares\\\\The\ equation:\\\\x^2+(x+2)^2=100\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\x^2+x^2+2(x)(2)+2^2=100\\\\2x^2+4x+4=100\qquad\text{subtract 100 from both sides}\\\\2x^2+4x-96=0\qquad\text{divide both sides by 2}\\\\x^2+2x-48=0\\\\x^2+8x-6x-48=0\\\\x(x+8)-6(x+8)=0\\\\(x+8)(x-6)=0\iff x+8=0\ \vee\ x-6=0\\\\x=-8<0\ \vee\ x=6\\\\x+2=6+2=8\\\\Answer:\ 8\ cm\ and\ 6\ cm.`