Question

PLEASE HELP!!!!

Answer 1

Answer:

Mike is not right

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----> surface area of the enlarged rectangular prism

y-----> surface area of the original rectangular prism

$z^{2}=\frac{x}{y}$

so

In this problem we have

$z=2$

substitute

$2^{2}=\frac{x}{y}$

$4=\frac{x}{y}$

$x=4y$

so

The surface area of the enlarged rectangular prism is 4 times the surface area of the original rectangular prism

therefore

Mike is not right

Verify with an example

we have a rectangular prism

$L=5\ m$

$W=2\ m$

$H=3\ m$

The surface area of the prism is equal to

$SA=2(LW)+(2L+2W)H$

substitute the values

$SA=2*(5*2)+(2*5+2*2)*3=62\ m^{2}$

If he doubles each dimension of any rectangular prism

then

the new dimensions will be

$L=5*2=10\ m$

$W=2*2=4\ m$

$H=3*2=6\ m$

The new surface area will be

$SA=2*(10*4)+(2*10+2*4)*6=248\ m^{2}$

$248/62=4$

therefore

The surface area of the enlarged rectangular prism is 4 times the surface area of the original rectangular prism