Question

the surface area of a package box is 56 sq inches. What is the surface area of a similar box that is larger by a scale factor of 3

Answer 1

Suppose it has length, width, height is \(l,w,h\) respectively.
\[
P = 2lw+2wh+2lh
\]

Answer 2

We change them to \(3l, 3w, 3h\): \[\begin{split}
P_2
&= 2(3l)(3w) + 2(3w)(3h) + 2(3l)(3h) \\
&= 2(9)lw + 2(9)wh + 2(9)lh \\
&= 9 ( 2lw + 2wh + 2lh) \\
&= 9P
\end{split}
\]

Answer 3

So\[
P_2 = 9P = 9(56)
\]

Answer 4

Thank you