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The area of a parallelogram is A=bh. We are given that the height is x-5, the base is x+5 and that the area of the figure is 56 square miles. So,

56=(x-5)(x+5)
Multiply x-5 and x+5
56=x²-25
Add 25 to both sides
81=x²
Take the square root of both sides
x=9

With the value of x, we can substitute it into the height and base so,

Height:9-5
Base=9+5

So, the height is 4miles and the base is 14 miles.
We can check the answer by using the formula of the area of a parallelogram. 
A=bh
56=4*14
56=56
ali015
The equation for the area of a parallelogram is: [tex]A = bh[/tex]
A = area, b = length of base, h = height

You are told that the height, h = x - 5, and base, b = x + 5. You are also told that the area is 56.

1) Plug these values into the equation. Multiply (x-5) and (x+5) by foiling:
[tex]A = bh\\ 56 = (x+5)(x-5)\\ 56 = x^{2} + 5x -5x + 5(-5)\\ 56 = x^{2} - 25[/tex]

2) Solve for the value of x
[tex]56 = x^{2} - 25\\ 56 + 25 = x^{2} \\ x^{2} = 81\\ x = \sqrt{81} \\ x = 9[/tex]
Note that x could also equal -9, but since we're looking for lengths of a shape, the lengths can't be negative!

3) Plug the value of x = 9 miles back into the equations for height and base to find the length of the base and height:
[tex]\text{height} = x-5 = 9 - 5 = 4\\\\ \text{base}= x+5 = 9 + 5 = 14[/tex]

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Answer: Height = 4 miles, Base = 14 miles

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