What is the surface area of the box if it is scaled up by a factor of 10? give that the surface area is: 272 in 2. length: 12 in 2 width: 8 in 2 height: 2 1/2 in 2

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-----> the scale factor

x-----> the surface area of the dilated box

y ---> the surface area of the original box

so

we have

substitute and solve for x

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: