Question

a) Calculate the scale factor from shape A to shape B. b) Find the value of t. Give each answer as an integer or as a fraction in its simplest form. ​

Answer 1

Answer is
80% or a dilation rate of .8
t = 5.6 cm

Explanation

Take your similar side measurement of your image and divide it by the pre image to get your dilation rate

4 / 5 = .8
12 / 15 = .8

.8 is your dilation rate

Your unknown “t” can be found using
7 cm x .8 dilation rate = 5.6 cm

Answer 2

a) The scale factor is
`(4)/(5)`

b)
`t=5(3)/(5)`

Explanation:

The scale factor from shape A to shape B is the value that is multiplied by the side measures of shape A to arrive at the side measures of shape B.

In other words, 5 times a certain value is 4, 15 times a certain value is 12. and 7 times a certain value is t.

Let's start by calling our "certain value" k.

`5k=4=\\k=(4)/(5)`

Let's check 15 to make sure k is 4/5, like so:

`15((4)/(5))=\\(60)/(5) =\\12`

Since 15 times 4/5 is twelve, our initial answer was correct.

So, the scale factor, or k, is 4/5.

Following this logic, we know that 7 multiplied by the scale factor is equal to t.

Let's set up an equation and solve for t:

`7((4)/(5) )=t=\\(28)/(5) =t=\\5(3)/(5) =t`

So,
`t=5(3)/(5)`