Question

Can you please help me out with a question

Answer 1

To determine the green rectangle, each side of the blue rectangle was multiplied by a determined scale factor k.

To determine the measure of x, the first step is to determine the scale factor.

The information that you have to use is the areas of both rectangles.

After dilation, the area of the resulting shape is equal to the area of the original shape multiplied by the square of the scale factor:

`A_{\text{green}}=k^2A_{\text{blue}}`

A.green=50 m²

A.blue= 72m²

`50=72k^2`

-Divide both sides by 72

`\begin{gathered} (50)/(72)=(72k^2)/(72) \\ (25)/(36)=k^2 \end{gathered}`

-Apply the square root to both sides of the equal sign:

`\begin{gathered} \sqrt[]{(25)/(36)}=\sqrt[]{k^2} \\ (5)/(6)=k \end{gathered}`

Now, to determine the value of x, multiply the length of the corresponding side on the blue rectangle by the scale factor:

`\begin{gathered} x=(5)/(6)\cdot12 \\ x=10 \end{gathered}`

The length of the side on the green triangle is 10m