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 * side`

`= \tt 4 * 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 * side`

`= \tt4 * 6`

`= \tt 24 \: cm`

Thus, the perimeter of this square = 24 cm

Ratio of the perimeters of both the squares :

`= \tt16 : 24`

`= \tt (16)/(24)`

`= \tt (16 / 4)/(24 / 4)`

`= \tt (4)/(6)`

`= \tt (4 / 2)/(6 / 2)`

`= \tt (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 * side`

`= \tt 4 * 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 * side`

`= \tt 6 * 6`

`= \tt{36cm}^(2)`

Thus, the area of the second square = 36 cm²

Ratio of the areas of the two squares :

`= \tt16 : 36`

`= \tt (16 / 4)/(36 / 4)`

`= \tt (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.