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the length of the side of two squares are 4cm and 6cm .Find in its simplest form the ratio of them perimeter and area​

Sagot :

LadyStrange

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.

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