The area of a parallogram is 128 sq miles . Find its base &height . 2x-4. 2x+ 4

A = (2x-4)(2x+4) = 128.

4x^2-16 = 128
4x^2 = 144
x^2 = 36
X = +-6.

2x-4 = 2*6 - 4 = 8 Mi. = Ht.
2x+4 = 2*6 + 4 = 16 Mi = Base.
.

To find the base and height of a parallelogram with a given area, we need to use the formula A = base * height, where A is the area of the parallelogram.

In this case, the area of the parallelogram is given as 128 sq miles.

Let's use the given values of the expressions for the base and height: base = 2x - 4 and height = 2x + 4.

Substituting the values into the formula, we have:

128 = (2x - 4) * (2x + 4)

Now we can solve the equation for x.

Expanding the equation:

128 = 4x^2 - 16

Rearranging the equation:

4x^2 = 128 + 16

4x^2 = 144

Dividing both sides by 4:

x^2 = 36

Taking the square root of both sides:

x = ±6

Since the base and height cannot be negative values, we can conclude that x = 6.

Now we can substitute the value of x back into the expressions for the base and height to find their values:

base = 2x - 4 = 2(6) - 4 = 12 - 4 = 8

height = 2x + 4 = 2(6) + 4 = 12 + 4 = 16

Therefore, the base of the parallelogram is 8 and the height is 16.

To find the base and height of a parallelogram, we need to use the formula for calculating its area.

The formula for the area of a parallelogram is A = base * height, where A represents the area, and base and height represent the respective measurements.

Given that the area of the parallelogram is 128 sq miles, we can set up the equation:

128 = base * height

Since we have two equations representing the base and height of the parallelogram: base = 2x - 4 and height = 2x + 4, we can substitute these values into the area equation:

128 = (2x - 4) * (2x + 4)

To solve this quadratic equation, we can expand the equation:

128 = 4x^2 - 16

Rearranging the equation:

4x^2 = 128 + 16
4x^2 = 144

Now, divide both sides of the equation by 4 to isolate x:

x^2 = 36

Taking the square root of both sides:

x = ±6

Since we are looking for positive values, x = 6.

Now we can substitute this value back into the base and height equations to find their values:

base = 2x - 4 = 2(6) - 4 = 12 - 4 = 8

height = 2x + 4 = 2(6) + 4 = 12 + 4 = 16

Therefore, the base of the parallelogram is 8 miles and the height is 16 miles.