Question

The square has a perimeter of 160 cm if the square is dilated with a scale factor of 0.9 what is the length of each side of the dilated Square in centimeters

Answer 1

36cm

Explanation:

Given: The square has a perimeter of
`160\text{cm}` ,the square is dilated with a scale factor of
`0.9`.

To Find: length of each side of the dilated square.

Solution:

Perimeter of square
`=160\text{cm}`

length of each side of perimeter
`=\frac{\text{perimeter of square}}{4}`

`=40\text{cm}`

Now,

the square is dilated by scale factor
`0.9`

new perimeter of square
`=\text{old perimeter}*\text{scale factor}`

`=160*0.9`

`=144\text{cm}`

new length of each side of square
`=\frac{\text{perimeter}}{4}`

`=(144)/(4)`

`=36\text{cm}`

Hence the length of each side of dilated square is
`36\text{cm}`

Answer 2

Answer: 36 cm

Explanation:

Given : The square has a perimeter =160 cm.

Perimeter of square = 4 (side)

Therefore , the side of square = (Perimeter)÷ 4

= 160 ÷ 4 = 40 cm

The new length of side after dilation = (Scale factor) x (Length of original figure)

For scale factor = 0.9

The new length of each side of the dilated square = (0.9)x(40)=36 cm

Hence, the new length of each side of the dilated square= 36 cm