Question

What is the surface area of 286.5 inches squared scaled up by a factor of 10

Answer 1

Answer:

28,650 in^2

Step-by-step explanation:

I assume the scaling up is of the linear dimensions.

Let's say you have a rectangle with length and width L and W.

The area of the rectangle is LW. We are told the area is 286.5 in^2.

Now we have

LW = 286.5 in^2

When you scale up the length and width by a factor of 10, both the length and width become 10 times greater.

The new length is now 10L.

The new width is now 10W.

The area of the new scaled up rectangle is

A = 10L * 10W = 100LW = 100(LW)

We were told LW = 286.5 in^2, so

the new area A = 100(286.5 in^2) = 28,650 in^2

Since the linear dimensions were scaled up by a factor of 10, the area increased by a factor of 10^2, or 100 times.

In general, when the linear dimensions are scaled up by a factor of k, the area increases by a factor of k^2.