Area of smaller square : Area of larger square = 4 : 49
Perimeter of small square = [tex]P_1[/tex]
Perimeter of large square = [tex]P_2[/tex]
P = 4L
[tex]P_1=4L_1\\\\P_2=4L_2[/tex]
Perimeter Ratio = 2:7
[tex]\frac{4L_1}{4L_2} =\frac{2}{7} \\\\\frac{L_1}{L_2} =\frac{2}{7}[/tex]
Area of a square = Length^2
[tex](\frac{L_1}{L_2} )^2=(\frac{2}{7} )^2\\\\\frac{L_{1} ^{2} }{L_{2} ^{2}} =\frac{2^2}{7^2} \\\\\frac{L_{1} ^{2} }{L_{2} ^{2}} =\frac{4}{49}[/tex]
Therefore, the ratio of the area of the smaller square to the area of the larger square = 4 : 49
Learn more on perimeters and area of squares here: https://brainly.com/question/25092270
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