Length of side of a square = 4cm
Perimeter of this square :
[tex] = \tt4 \times side[/tex]
[tex] = \tt 4 \times 4[/tex]
[tex] = \tt16 \: cm[/tex]
Thus, the perimeter of this square = 16 cm
Length of side of the second square = 6 cm
Perimeter of this square :
[tex] = \tt 4 \times side[/tex]
[tex] = \tt4 \times 6[/tex]
[tex] = \tt 24 \: cm[/tex]
Thus, the perimeter of this square = 24 cm
Ratio of the perimeters of both the squares :
[tex] = \tt16 : 24[/tex]
[tex] = \tt \frac{16}{24} [/tex]
[tex] = \tt \frac{16 \div 4}{24 \div 4} [/tex]
[tex] = \tt \frac{4}{6} [/tex]
[tex] = \tt \frac{4 \div 2}{6 \div 2} [/tex]
[tex] = \tt \frac{2}{3} [/tex]
Thus, the ratio of the perimeter of both the squares = 2:3
Length of side of the first square = 4 cm
Area of this square :
[tex] = \tt side \times side[/tex]
[tex] = \tt 4 \times 4[/tex]
[tex] = \tt {16cm}^{2} [/tex]
Thus, the area of the first square = 16 cm²
Length of side of the second sqaure = 6 cm
Area of this square :
[tex] = \tt \: side \times side[/tex]
[tex] = \tt 6 \times 6[/tex]
[tex] = \tt{36cm}^{2} [/tex]
Thus, the area of the second square = 36 cm²
Ratio of the areas of the two squares :
[tex] = \tt16 : 36[/tex]
[tex] = \tt \frac{16 \div 4}{36 \div 4} [/tex]
[tex] = \tt \frac{4}{9} [/tex]
[tex] = \tt4 : 9[/tex]
Thus, the ratio of the areas of the two squares = 4:9
Therefore, the ratio of the perimeter of the squares = 2:3 and the ratio of the areas of these squares = 4:9.
