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Alexeev081 [22]
1 year ago
13

The area of the parallelogram is 56 square miles. Find its base and height.

Mathematics
2 answers:
Verdich [7]1 year ago
8 0
The equation for the area of a parallelogram is: A = bh
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:
A = bh\\
56 = (x+5)(x-5)\\
56 =  x^{2} + 5x -5x + 5(-5)\\
56 =  x^{2} - 25

2) Solve for the value of x
56 = x^{2} - 25\\
56 + 25 = x^{2} \\
 x^{2} = 81\\
x =  \sqrt{81} \\
x = 9
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:
\text{height} = x-5 = 9 - 5 = 4\\\\
\text{base}= x+5 = 9 + 5 = 14

--------

Answer: Height = 4 miles, Base = 14 miles
Andru [333]1 year ago
3 0
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
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