The area of a rectangle is 128 square feet. Its height is twice its base. Find the length of the height and the length of the base.
h = 2b
h * b = 2b * b = 128
Solve for b, then h.
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To find the length of the height and the length of the base of the rectangle, let's set up some equations based on the given information.
Let's assume that the length of the base of the rectangle is 'x' feet.
According to the given information, the height of the rectangle is twice its base. So the height would be '2x' feet.
The area of a rectangle is calculated by multiplying its length and width. As the length of the base is 'x' feet and the height is '2x' feet, the area of the rectangle can be expressed as:
Area = Length * Width
= (x) * (2x)
= 2x^2
Given that the area of the rectangle is 128 square feet, we can set up the equation as:
2x^2 = 128
Let's solve this equation to find the values of 'x' and '2x'.
2x^2 = 128
Divide both sides of the equation by 2:
x^2 = 64
Take the square root of both sides:
√(x^2) = ±√(64)
x = ±8
Since length cannot be negative, we discard the negative value.
So, the length of the base of the rectangle, 'x', is 8 feet.
Now, to find the length of the height, which is twice the length of the base, we multiply 'x' by 2:
Height = 2x
= 2 * 8
= 16
Therefore, the length of the base is 8 feet and the length of the height is 16 feet.