A square painting painting is surrounded by a frame. the outside edges of the frame are 3 inches in length, and the frame is 3 i
1 answer:
Answer:
Area = 36
Step-by-step explanation:
There must be an error with the statement, because it is strange that the length of the frame is equal to its thickness.
Assuming that the data supplied is correct, we can do the following procedure.
Let's call L the length of the frame.
We know how much each side of the square measures.
L = 3 inches
We also know that the thickness (s) is:
s = 3 inches.
Then the area of the frame is equal to:
Area = Perimeter * thickness
Area = 4L*s
Area = 3*4*3
Area = 36
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The base length that will maximize the area for such a window is 168.03 cm. The exact largest value of x when this occurs is 233.39 cm
Suppose we make an assumption that:
- (x) should be the width of the rectangle base;
- (h) should be the height of the rectangle
Also, provided that the diameter of the semi-circle appears to be the base of the rectangle, then;
- the radius
and, the perimeter of the window can now be expressed as:
Given that the perimeter = 600 cm
∴
Since h > 0, then:
By rearrangement and using the inverse rule:
Thus, the largest length x = 233.39 cm
However, the area of the window is given as:
Now, at maximum, when the area A = 0. Taking the differentiation, we have:
Making x the subject of the formula, we have:
x = 168.03 cm
Taking the second derivative:
Therefore, we can conclude that the maximum area that exists for such a window is 168.03 cm
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