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Question
If a picture is placed in a frame 2 inches wide and frame area is 87 square inches, what are picture dimensions?

Let:
L- Length

W- Width


Dimensions of frame:

Length- 10.25 inches *
Width- 8.5 inches *

* 8 x 10 frame.

Frame- 2 inches wide

Frame area- 87 in.^2


Picture dimensions:

Length- 6.5 inches *

Width- 4.5 inches *


* 4 x 6 picture


I was attempting to use the formula to calculate with actually measuring frame and picture.

Which measurement to use for length is X larger than width for frame?

10.25/8.5 = 1.20

8/5/10.25 = .829

10.25-8.5 = 1.75


My solution (not sure):

L X W = LW Total Area of frame and picture.

(L-4)(W-4)= LW - 4W - 4L + 16 in.^2

LW - (LW - 4W - 4L + 16) = 87

4W + 4L = 103

W + L = 25.75

How do I proceed from here?

Thanks.

Answer
"If a picture is placed in a frame 2 inches wide and frame area is 87 square inches, what are picture dimensions?"
You can't tell, because there are an infinite number of solutions.

Let L and W be the length and width of the picture.
The frame will have a 4" square in each corner, contributing 16 inē of area.

remaining area of frame = 2(2L) + 2(2W) = 4(L+W)
4(L+W) = 87 - 16 = 71 inē
L+W = 71/4 = 17.75 in
W = 17.75 - L
The picture can have any positive length less than 17.75".

For example, if the picture is 10" long then its width is 7.75" and area = 77.5 inē.
area of picture + frame = (10+4)(7.75+4) = 164.5 inē
area of frame = 164.5 - 77.5 = 87 inē

If the picture is 9" long then its width is 8.75 and area = 78.75 inē.
area of picture + frame = (9+4)(8.75+4) = 165.75 inē
area of frame = 165.75 - 78.75 = 87 inē

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