Question

finding scale factor
scale factor is a ratio between the side - length measurements of two similar figures. scaling a figure up means that the ratio is greater than one. scaling a figure down means the ratio is less than one. compare the side lengths that are similar by using a ratio in fraction form. simplify or divide that fraction to find your scale factor.
scale factor: side length of new shape divided by corresponding side length of old shape
\\(\frac{new\\ shape}{old\\ shape}=\frac{10\\ cm}{5\\ cm}=2\\)
use the scale factor provided to find the side lengths of the new figure. show all your work. (shapes are not drawn to scale)
#1
scale factor: 3
#2
scale factor: 1/2
#3
scale factor: 4

Explanation:

Step1: Recall scale - factor formula

The scale factor \(k\) is given by \(k=\frac{\text{side length of new shape}}{\text{corresponding side length of old shape}}\).

Step2: Solve for #1

For the first rectangle, the old - rectangle has sides 6 ft and 8 ft, and the scale factor \(k = 3\).
The new side lengths are:
For the side corresponding to 6 ft: \(6\times3=18\) ft.
For the side corresponding to 8 ft: \(8\times3 = 24\) ft.

Step3: Solve for #2

The old - rectangle has sides 2 cm and 10 cm, and the scale factor \(k=\frac{1}{2}\).
The new side lengths are:
For the side corresponding to 2 cm: \(2\times\frac{1}{2}=1\) cm.
For the side corresponding to 10 cm: \(10\times\frac{1}{2}=5\) cm.

Step4: Solve for #3

The old - rectangle has sides 1 in and 1.5 in, and the scale factor \(k = 4\).
The new side lengths are:
For the side corresponding to 1 in: \(1\times4=4\) in.
For the side corresponding to 1.5 in: \(1.5\times4 = 6\) in.

Answer:

For #1: New side lengths are 18 ft and 24 ft.
For #2: New side lengths are 1 cm and 5 cm.
For #3: New side lengths are 4 in and 6 in.