Question

A rectangle has a length of 7.5 inches and a width of 3 inches. This rectangle is dilated by a scale factor of 2.2 to create a new rectangle. What are the dimension of the new rectangle? Length and Width

Answer 1

For this case is the rectangle is dilated a factor of 2.2 we assume that the expansion is in all the dimensions so then the new length and width are:

`L_f = 2.2 L_i= 2.2* 7.5 in = 16.5 in`

`W_f = 2.2 w_i = 2.2 * 3 in = 6.6 in`

Explanation:

The area of a rectangle is given by
`A = L *W`

For this case is the rectangle is dilated a factor of 2.2 we assume that the expansion is in all the dimensions so then the new length and width are:

`L_f = 2.2 L_i= 2.2* 7.5 in = 16.5 in`

`W_f = 2.2 w_i = 2.2 * 3 in = 6.6 in`

And the area would be (2.2)^2 times the initial area since is defined as
`A = L_f W_f`

Answer 2

The length and the width of the new rectangle are 16.5 inches and 6.6 inches respectively

Explanation:

Given

Shape: Rectangle

`Length = 7.5 inches`

`Width = 3 inches`

`Scale factor = 2.2`

Required

Dimension of the new rectangle

The dimensions of the new rectangle can be solved by multiplying the scale factor by the old dimensions;

This means that

New Length = Scale factor * Old Length

and

New Width = Scale factor * Old Width

Calculating the new length

New Length = Scale factor * Old Length

Substitute 2.2 for scale factor and 7.5 for old length; This gives

`New Length = 2.2 * 7.5 inches`

`New Length = 16.5 inches`

Calculating the new width

New Width = Scale factor * Old Width

Substitute 2.2 for scale factor and 3 for old width; This gives

`New Width = 2.2 * 3 inches`

`New Width= 6.6 inches`

Hence, the length and the width of the new rectangle are 16.5 inches and 6.6 inches respectively