A square has the same area as a rectangle whose longer side is 2 times the length of its shorter side. If the perimeter of the rectangle is 24, what is the perimeter of the square?
A. 8 sqrt 2
B. 16 sq
(x+x) + (2x+2x) - 24,
X = 4.
2x = 8.
Ar = L*W = 8 * 4 = 32. = As.
S^2 = 32,
s = 4sqrt 2.
Ps = 4 * 4sqrt2 = 16 sqrt2.
Sorry these are the answer choices:
A. 8 sqrt 2
B. 16 sqrt 2
C. 32 sqrt 2
D. 32
I got B
good
The perimeter of the rectangle is given as 24, which means that the sum of all its sides is 24. Let's call the length of the shorter side of the rectangle "x". This means that the length of the longer side is 2x.
The perimeter of the rectangle is then calculated as follows:
Perimeter = 2*(length + width)
Perimeter = 2*(x + 2x)
24 = 2*(3x)
24 = 6x
x = 4
Now that we know the length of the shorter side is 4, we can find the length of the longer side: 2x = 2*4 = 8.
The area of the square is equal to the area of the rectangle: x^2 = 4^2 = 16.
To find the perimeter of the square, we need to find the length of one side. Since the area of the square is 16, the side length of the square is the square root of 16, which is 4.
Finally, we calculate the perimeter of the square: Perimeter = 4 * side length = 4 * 4 = 16.
Therefore, the perimeter of the square is 16, which corresponds to option B. 16 sq.
To find the perimeter of the square, we first need to find the dimensions of the rectangle.
Let's assume that the shorter side of the rectangle is x. Therefore, the longer side of the rectangle would be 2x.
The area of a square is given by s^2, where s is the length of one side.
Since the square has the same area as the rectangle, we can set up the following equation:
s^2 = x * 2x
Simplifying this equation gives us:
s^2 = 2x^2
Now, let's find the dimensions of the rectangle based on the given perimeter.
The perimeter of a rectangle is given by the formula: 2 * (length + width).
Given that the perimeter of the rectangle is 24, we can set up the following equation:
2 * (x + 2x) = 24
Simplifying this equation gives us:
6x = 24
Solving for x gives us: x = 4
Now that we know x = 4, we can substitute this value back into the equation to find the side length, s, of the square:
s^2 = 2(4^2)
s^2 = 2(16)
s^2 = 32
Taking the square root of both sides gives us:
s = sqrt(32)
Simplifying this expression gives us:
s = 4 * sqrt(2)
Finally, to find the perimeter of the square, we multiply the side length by 4 (since a square has all sides equal):
Perimeter of the square = 4 * s
Perimeter of the square = 4 * (4 * sqrt(2))
Perimeter of the square = 16 * sqrt(2)
Therefore, the perimeter of the square is 16 * sqrt(2).
The correct answer is option B: 16 * sqrt(2).
so what did you get ?
what was your solution?