Question

1) IF the area of the frame was 64inches², what would be 2 possible sets of dimensions that could be used to make a frame with that area?
Set 1:

Set 2:

Explain your thinking:

1) The frame is being enlarged to hang on a gallery wall. Using the scale factor of 1in=2.5ft., give the new dimensions of the outside edges of the frame. Explain and show your work! Work:



Explain your thinking:




New Dimensions: 5in. = ___________ 7in=___________

Answer 1

There are infinite possibilities for this answer, let's see how:
Assuming the frame is rectangular, and it has 64 square inches, then the multiplication of the height (H) and width (W) is 64.
So H*W=64, therefore H=64/W
Any pair of numbers that fits this equation will be a possible answer.
A few examples:
H=1; W=64
H=2; W=32
H=1,23456; W= 51,840338
H=4; W=16
H=8; W=8
etc.

So, for example, one set can be 8x8 inches
another set can be 4x16 inches

if the frame were to have 5 inches and 7 inches, since 1 inch correponds to 2.5ft, then we simply must multiply the values in inches per 2.5 to get the values in feet, then it would correspond to
5*2.5=12.5 ft  and   7*2.5=17.5 ft