the area of the parallelogram is 96 square miles. Find its base and height. if the base is x+5 and the height is x-5
To find the base and height of a parallelogram when given its area, we can use the formula:
Area = base × height
Given that the area of the parallelogram is 96 square miles, and the base is (x+5) and the height is (x-5), we can set up the equation:
96 = (x+5) × (x-5)
Now, let's solve for x:
96 = x^2 - 25 (using the difference of squares)
Add 25 to both sides:
121 = x^2
Take the square root of both sides:
±11 = x
Since we are looking for the positive value of x, x = 11.
Now, substitute this value back into the base and height equations:
Base = x + 5 = 11 + 5 = 16 miles
Height = x - 5 = 11 - 5 = 6 miles
Therefore, the base of the parallelogram is 16 miles and the height is 6 miles.
To find the base and height of a parallelogram, you first need to understand the formula for the area of a parallelogram.
The formula to find the area of a parallelogram is:
Area = base * height
Given that the area is 96 square miles, and the base is x+5 and height is x-5, we can substitute these values into the formula:
96 = (x+5) * (x-5)
Now, let's solve this equation to find the value of x.
First, expand the equation:
96 = x^2 - 25
Rearrange the equation:
x^2 = 96 + 25
x^2 = 121
Now, take the square root of both sides to solve for x:
x = ±√121
x = ±11
Since lengths cannot be negative, we can discard the negative value.
Therefore, x = 11.
Now that we have the value of x, we can substitute it back into the expressions for the base and height:
Base = x + 5 = 11 + 5 = 16
Height = x - 5 = 11 - 5 = 6
So, the base of the parallelogram is 16 units and the height is 6 units.
b * h = 96
(x + 5)(x - 5) = 96
Solve for x.