Question

I don’t need any work shown just an answer! Thank you so much!!A toothpaste manufacturer wraps its boxes in plastic. Its most popular toothpaste comes in a box that’s 8 centimeters tall and uses 1,224 square centimeters of plastic wrap. The company sells a travel version of the toothpaste in a box that’s a dilation of the original box. The travel version uses 306 square centimeters of plastic wrap. How tall is the travel version’s box?

Answer 1

Its most popular toothpaste comes in a box that’s 8 centimeters tall and uses 1,224 square centimeters of plastic wrap.

The travel version uses 306 square centimeters of plastic wrap.

How tall is the travel version’s box?

First, we need to find out the scale factor for the dilation

`\begin{gathered} scaled\: area=(scale\: factor)^2* original\: area \\ (scale\: factor)^2=(scaledarea)/(originalarea) \\ (scale\: factor)^2=(306)/(1224) \\ (scale\: factor)^2=(1)/(4) \\ scale\: factor^{}=\sqrt{(1)/(4)} \\ scale\: factor^{}=(1)/(2) \end{gathered}`

So, the scale factor is 1/2

Now we can easily find the height of the travel version's box as

`\begin{gathered} scaled\: height=scale\: factor^{}* original\: height \\ scaled\: height=(1)/(2)*8 \\ scaled\: height=4\: cm \end{gathered}`

Therefore, the scaled height of the travel version's box is 4 cm