Question

Help please :)
A triangular prism has a length of 12 inches. A larger similar triangular prism has a length of 16 inches.



If 216 square inches of paper is used to wrap the smaller prism with minimum wastage, approximately how many square inches of paper will be required to wrap the larger prism?

Answer 1

if correct please click best response.

Answer 2

where did the 8^2 come from in that first line?

Answer 3

I could be wrong, but I would have thought it would go like this...

To me, "wrapping the prism" means covering the three rectangular sides, not the two triangular parts at the top and bottom.

So that side area for a single side would be Length X Width, and there are 3 sides, so it would be 3LW.

For the small prism, with L = 12, 3LW = 3(12)W = 216
for the large prism, with L = 16, 3LW = 3(16)W = ??

The 3 and the W cancel, so you do that, then you cross multiply:
12/16 = 216/x

12x = 3456

x = 288

Answer 4

(12^2)/(16^2) = 216/x


144/256 = 216/x


144x = 256*216


144x = 55296


x = 55296/144


x = 384


So the surface area of the larger prism is 384 square inches.

Answer 5

why do you square the lengths?

Answer 6

Are you assuming the lengths and base sides are the same length?

Answer 7

the key word is "similar"

Answer 8

I assumed the base shapes were identical, and the only thing that changed was the length. But I wasn't sure how to interpret "similar prism"

Answer 9

So the corresponding sides form a ratio.

Answer 10

I didn't know if that terminology applied to a solid.