<h2>
Hello!</h2>
The answer is:
The dimensions of the paper for Gift C, are: 25" x 12"
and its area is:
![GiftCArea=300inch^{2}](https://tex.z-dn.net/?f=GiftCArea%3D300inch%5E%7B2%7D)
<h2>
Why?</h2>
To solve the problem, we need to calculate the total area of the remaining paper, and then, subtract it from the paper used for the gift A and B.
We know that:
![GiftA=TotalPaperArea*\frac{2}{5}\\\\GiftB=TotalPaperArea*\frac{1}{3}](https://tex.z-dn.net/?f=GiftA%3DTotalPaperArea%2A%5Cfrac%7B2%7D%7B5%7D%5C%5C%5C%5CGiftB%3DTotalPaperArea%2A%5Cfrac%7B1%7D%7B3%7D)
Now, the paper for Gift C will be:
![GiftCArea=(TotalPaperArea)-(PaperArea*\frac{2}{5}+PaperArea*\frac{1}{3})](https://tex.z-dn.net/?f=GiftCArea%3D%28TotalPaperArea%29-%28PaperArea%2A%5Cfrac%7B2%7D%7B5%7D%2BPaperArea%2A%5Cfrac%7B1%7D%7B3%7D%29)
From the statement we know that the dimenstions of the remaining paper are 25" x 45", so calculating the area we have:
![TotalArea=25inch*45inch=1125inch^{2}](https://tex.z-dn.net/?f=TotalArea%3D25inch%2A45inch%3D1125inch%5E%7B2%7D)
Now, calculating the area of the paper for Gift A and B, we have:
![GiftA=1125inch^{2}*\frac{2}{5}=450inch^{2}\\\\GiftB=1125inch^{2}*\frac{1}{3}=375inch^{2}](https://tex.z-dn.net/?f=GiftA%3D1125inch%5E%7B2%7D%2A%5Cfrac%7B2%7D%7B5%7D%3D450inch%5E%7B2%7D%5C%5C%5C%5CGiftB%3D1125inch%5E%7B2%7D%2A%5Cfrac%7B1%7D%7B3%7D%3D375inch%5E%7B2%7D)
Then, calculating the paper for Gift C, we have:
![GiftCArea=(TotalPaperArea)-(PaperArea*\frac{2}{5}+PaperArea*\frac{1}{3})](https://tex.z-dn.net/?f=GiftCArea%3D%28TotalPaperArea%29-%28PaperArea%2A%5Cfrac%7B2%7D%7B5%7D%2BPaperArea%2A%5Cfrac%7B1%7D%7B3%7D%29)
![GiftCArea=1125inch^{2}-(450inch^{2}+375inch^{2}+)](https://tex.z-dn.net/?f=GiftCArea%3D1125inch%5E%7B2%7D-%28450inch%5E%7B2%7D%2B375inch%5E%7B2%7D%2B%29)
![GiftCArea=1125inch^{2}-825inch^{2}=300inch^{2}](https://tex.z-dn.net/?f=GiftCArea%3D1125inch%5E%7B2%7D-825inch%5E%7B2%7D%3D300inch%5E%7B2%7D)
![GiftCArea=300inch^{2}](https://tex.z-dn.net/?f=GiftCArea%3D300inch%5E%7B2%7D)
Therefore, calculating the dimensions of the paper for Gift C, knowing the height of the paper (25inches), we have::
![GiftCArea=Height*Width\\\\Width=\frac{GiftCArea}{25inches}=\frac{300inches^{2} }{25inches}=12inches](https://tex.z-dn.net/?f=GiftCArea%3DHeight%2AWidth%5C%5C%5C%5CWidth%3D%5Cfrac%7BGiftCArea%7D%7B25inches%7D%3D%5Cfrac%7B300inches%5E%7B2%7D%20%7D%7B25inches%7D%3D12inches)
Hence, the dimensions of the paper for Gift C, are: 25" x 12".
Have a nice day!