The geometric support of a design is given by a large and a small square. If you want the total area of the figure to be 97 cm^2 and its perimeter 44 CM. What measurements should the sides of the squares have?

Let A be the side of larger square and a be the side of smaller scale, then $$ A^2+a^2=97 \: \: .... (1)$$ Perimeter is $$ 4A+2a=44 $$ or$$ 2A+a=22 $$ $$ a=22-2A $$ Substituting it in eqn. (1), we have $$ A^2+\left(22-2A\right)^2=97 $$ $$ A^2+484+4A^2-88A=97 $$ $$ 5A^2-88A+387=0 $$ On solving, A = 9, 8.6 Any measurement out of these two will work. Taking A = 9 cm a = 22 - 2A = 22-18 = 4 cm