Hello!
The answer is:
The dimensions of the paper for Gift C, are: 25" x 12"
and its area is:
[tex]GiftCArea=300inch^{2}[/tex]
Why?
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:
[tex]GiftA=TotalPaperArea*\frac{2}{5}\\\\GiftB=TotalPaperArea*\frac{1}{3}[/tex]
Now, the paper for Gift C will be:
[tex]GiftCArea=(TotalPaperArea)-(PaperArea*\frac{2}{5}+PaperArea*\frac{1}{3})[/tex]
From the statement we know that the dimenstions of the remaining paper are 25" x 45", so calculating the area we have:
[tex]TotalArea=25inch*45inch=1125inch^{2}[/tex]
Now, calculating the area of the paper for Gift A and B, we have:
[tex]GiftA=1125inch^{2}*\frac{2}{5}=450inch^{2}\\\\GiftB=1125inch^{2}*\frac{1}{3}=375inch^{2}[/tex]
Then, calculating the paper for Gift C, we have:
[tex]GiftCArea=(TotalPaperArea)-(PaperArea*\frac{2}{5}+PaperArea*\frac{1}{3})[/tex]
[tex]GiftCArea=1125inch^{2}-(450inch^{2}+375inch^{2}+)[/tex]
[tex]GiftCArea=1125inch^{2}-825inch^{2}=300inch^{2}[/tex]
[tex]GiftCArea=300inch^{2}[/tex]
Therefore, calculating the dimensions of the paper for Gift C, knowing the height of the paper (25inches), we have::
[tex]GiftCArea=Height*Width\\\\Width=\frac{GiftCArea}{25inches}=\frac{300inches^{2} }{25inches}=12inches[/tex]
Hence, the dimensions of the paper for Gift C, are: 25" x 12".
Have a nice day!
