The surface area of a rectangular prism is 35 square inches. What is the surface area of a similar solid with dimensions that have been enlarged by a scale factor of 7?

Respuesta :

Answer:

[tex]1,715\ in^{2}[/tex]

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 figure

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

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=7[/tex]

[tex]y=35\ in^{2}[/tex]

substitute

[tex]7^{2}=\frac{x}{35}[/tex]

[tex]x=7^{2}(35)=1,715\ in^{2}[/tex]