Answer :
The ratio of the area of the smaller square to the area of the larger square = 4 : 49
Finding the area of a square from the perimeter
Let the perimeter of the small square be [tex]P_1[/tex]
Lethe the perimeter of the large square be [tex]P_2[/tex]
Perimeter of a square = 4 Length
[tex]P_1=4L_1\\\\P_2=4L_2[/tex]
The ratio of the perimeters = 2:7
[tex]\frac{4L_1}{4L_2} =\frac{2}{7} \\\\\frac{L_1}{L_2} =\frac{2}{7}[/tex]
The area of a square = L^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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