Question

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

Answer 1

Length of side of a square = 4cm

Perimeter of this square :

$= \tt4 \times side$

$= \tt 4 \times 4$

$= \tt16 \: cm$

Thus, the perimeter of this square = 16 cm

Length of side of the second square = 6 cm

Perimeter of this square :

$= \tt 4 \times side$

$= \tt4 \times 6$

$= \tt 24 \: cm$

Thus, the perimeter of this square = 24 cm

Ratio of the perimeters of both the squares :

$= \tt16 : 24$

$= \tt \frac{16}{24}$

$= \tt \frac{16 \div 4}{24 \div 4}$

$= \tt \frac{4}{6}$

$= \tt \frac{4 \div 2}{6 \div 2}$

$= \tt \frac{2}{3}$

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 :

$= \tt side \times side$

$= \tt 4 \times 4$

$= \tt {16cm}^{2}$

Thus, the area of the first square = 16 cm²

Length of side of the second sqaure = 6 cm

Area of this square :

$= \tt \: side \times side$

$= \tt 6 \times 6$

$= \tt{36cm}^{2}$

Thus, the area of the second square = 36 cm²

Ratio of the areas of the two squares :

$= \tt16 : 36$

$= \tt \frac{16 \div 4}{36 \div 4}$

$= \tt \frac{4}{9}$

$= \tt4 : 9$

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.