Question

27. A figure has a perimeter of 26 units. What will the new perimeter be after a dilation with a scale factor of 2.5?

Answer 1

65 units

Step-by-step explanation

Step 1

Let

current perimeter : 26 units

s.f: 2.5

The scale factor in the dilation of a mathematical object determines how much larger or smaller the image will be (compared to the original object),so

`\text{scale factor=}\frac{transformed\text{ figure}}{\text{original figure}}`

now, replace

`\begin{gathered} \text{scale factor=}\frac{transformed\text{ figure}}{\text{original figure}} \\ 2.5=\frac{transformed\text{ figure}}{26\text{ units}} \end{gathered}`

Finally, solve for transformed figure

`\begin{gathered} 2.5=\frac{transformed\text{ figure}}{26\text{ units}} \\ \text{ Mulitply both sides by 26} \\ 2.5\cdot26units=\frac{transformed\text{ figure}}{26\text{ units}}\cdot26\text{ units} \\ 65\text{ units = new perimeter} \end{gathered}`

therefore, the answer is

65 units

I hope this helps you