Geometry - Parallelogram Problem
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- DavidG@VeritasPrep
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The problem is that though side EC = 3x, side AB = 4x, so it isn't true that 3x * 3 = 21. (Side DC = x + 3x = 4x. Opposite sides of a parallelogram are equal, so DC = AB = 4x.)
So the shape ABCE is a trapezoid. Area of trapezoid = Height* (Base 1 + Base 2)/2
Base 1 = EC = 3x
Base 2 = AB = 4x
Height = 3
Area = 3* (3x + 4x)/2; we're told that this is 21
3* (3x + 4x)/2 = 21
Solving, we get x = 2.
So Base of parallelogram = 4x = 4*2 = 8
Height = 3
Base * Height = 8*3 = 24
(Or, thinking of it as you did, if x = 2, the area of the triangle would be (2*3)/2 = 3. 21 + 3 = 24.)
- ahmedshafea
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You can generally assume that most instructors' replies are either:ahmedshafea wrote:Is the above reply a correct solution? If not could one explain the steps please
1) right, or
2) wrong, but quickly corrected by another instructor looking to score on the first instructor
From those two statements, it more or less follows that an instructor's reply that hasn't been corrected by another instructor for years is probably right.