The diagram below represents a photograph in a frame. The photo has a perimeter of 23 inches, and the area of the whole figure is 58.5 square inches. If the frame is 1 inch thick, what is the area of the photo in square inches?
ok, lets say the length and width of the photo is l and w.
then, \(2\left(l+w\right)=23\)
and if the frame is 1 inch, \(\left(l+1+1\right)\left(w+1+1\right)=58.5\)
then we just solve the system of equations and get l = 7 and w = 4.5 so the area is 31.5
Do you understand what mworkhard has presented so far? I will assume so ....
2(L+W) = 23 (1)
(L+2)(W+2)=58.5 (2)
LW+2(W+L)+4=58.5
sub in (1)
LW+23+4=58.5
LW+27=58.5
LW=31.5
L=31.5/W
sub into (1) to find W
2(L+W) = 23 (1)
\(2(\frac{31.5}{W}+W) = 23 \\ \text{mult both sides by W}\\ 2W(\frac{31.5}{W}+W) = 23W \\ 63+2W^2=23W\\ 2w^2-23w+63=0\\ w=\frac{23\pm\sqrt{529-504}}{4}\\ w=\frac{23\pm\sqrt{25}}{4}\\ w=\frac{23\pm5}{4}\\ w=4.5\;or\; 7\)
Length = 7 width =4.5 inches
omg how did i not see this! Here is how u can solve the system:
Where I got my steps: https://www.symbolab.com/solver/step-bystep/2%5Cleft(l%2Bw%5Cright)%3D23%2C%20%5Cleft(l%2B1%2B1%5Cright)%5Cleft(w%2B1%2B1%5Cright)%3D58.5