Clint found the area of the parallelogram shown. Which statement explains the error Clint made?
2 answers:
Answer:
D
Step-by-step explanation:
The area of a parallelogram is denoted by: , where b is the base and h is the height that is perpendicular to the base. Depending on what kind of parallelogram it is (square, rectangle, rhombus, regular parallelogram), that height <em>could</em> be the side length, but usually it is not; it is only the side length in special cases, like a square.
Here, we are given that the base is 11 and that the height is 4. Since the problem gives us two different values for the height versus the side length, we know that for this parallelogram, the height is not the same as the side length. Thus, we must use 4 for the height and 11 for the base in the area formula.
Therefore, the only answer that correctly points out this mistake is D.
Hope this helps!
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The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
Let the area be y .
Area = (base) × (height)
Base = 2x
Height = h
Let the area of the rectangular pens be y .
∴ y = 2xh
Perimeter of all the fencing = 4x+3h
∴ 4x+3h = 120
now we solve for h
3h = 120-4x
h = 40 - 4/3 x
Now we will substitute this value in the above first equation:
y = 2xh
or, y = 2x (40 - 4/3 x)
or, y = 80x - 8/3 x²
Now for the maximum area we have to find the first order differentiation of y
now,
dy /dx = 80 - 16/3 x
At dy/dx = 0 we get the value of x for which y is maximum.
80 - 16/3 x = 0
or, - 16/3 x = -80
or, x = 15 feet
Hence height = 40 - 4/3 x = 40 - 20 = 20feet
Maximum area = 2xh = 2×15×40 = 1200 square feet
The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
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