A rectangular museum painting has a uniform width frame around it. The frame is 8 feet high by 10 feet long. If the diagonal of the painting is 10 feet, determine the width of the frame.
If the painting has length x and height y, and the frame has width w, then we have
x+2w = 10
y+2w = 8
x^2+y^2 = 100
Now just solve for w
To determine the width of the frame, we need to find the dimensions of the painting itself.
Let's define the width of the painting as "w" and the height of the painting as "h". Since the frame has a uniform width, the outer dimensions of the painting and frame combined will be (w + 2f) by (h + 2f), where "f" represents the width of the frame.
We are given that the frame is 8 feet high by 10 feet long, so we have the following equations:
h + 2f = 8 feet
w + 2f = 10 feet
Now, we need to find the dimensions of the painting itself. Using the Pythagorean theorem, we can relate the dimensions of the painting and the length of the diagonal:
(w + 2f)^2 + (h + 2f)^2 = diagonal^2
Substituting the given values:
(10 feet)^2 + (8 feet)^2 = (10 feet)^2
Simplifying the equation:
100 + 64 = 100
This is a contradiction, so the given information is incorrect. There is no valid solution to this problem.