A RECTANGLE HAS A WIDTH OF X CENTIMETERS AND A PERIMETER OF 8X CENTIMETERS. A SQUARE HAS SIDES OF LENGTH 1/4 THAT OF THE RECTANGLE

A) FIND THE LENGTH OF THE RECTANGLE
B) FIND THE PERIMETER OF THE SQUARE
C) FIND HOW MANY CCENTIMETERS GREATER THE RECTANGLE IS THAN THE SQUARES PERIMETER IF X=4
D) FIND HOW MANY SQUARE CENTIMETERS GREATER THEN RECTANGLE'S AREA IS THAN THE SQUARES AREA IF X=4

you mom

A) To find the length of the rectangle, we can use the formula for the perimeter of a rectangle, which is twice the sum of its width and length. Since the perimeter of the rectangle is given as 8X centimeters, we have the equation:

2(width + length) = 8X

We know that the width is X centimeters, so we substitute X for the width:

2(X + length) = 8X

Simplifying the equation:

2X + 2(length) = 8X

Subtracting 2X from both sides:

2(length) = 6X

Dividing both sides by 2:

length = 3X

Therefore, the length of the rectangle is 3X centimeters.

B) The length of the square is 1/4 of the length of the rectangle, which we found to be 3X centimeters. So the length of the square is (1/4)(3X) = 3/4X centimeters.

The perimeter of a square is given by 4 times the length of one side. Therefore, the perimeter of the square is:

4(3/4X) = 3X

So the perimeter of the square is 3X centimeters.

C) To find how many centimeters greater the rectangle is than the square's perimeter, we subtract the perimeter of the square from the perimeter of the rectangle:

8X - 3X = 5X

Therefore, the rectangle is 5X centimeters greater than the square's perimeter.

D) The area of the rectangle is given by the product of its width and length. The width of the rectangle is X centimeters and the length is 3X centimeters. So the area of the rectangle is:

width × length = X × 3X = 3X^2 square centimeters.

The area of a square is given by the square of its side length. The side length of the square is 3/4X centimeters, as we found earlier. So the area of the square is:

(side length)^2 = (3/4X)^2 = 9/16X^2 square centimeters.

To find how many square centimeters greater the rectangle's area is than the square's area, we subtract the area of the square from the area of the rectangle:

3X^2 - 9/16X^2 = 33/16X^2

Therefore, the rectangle's area is 33/16X^2 square centimeters greater than the square's area if X = 4.

To find the answers to the given questions, we need to follow a step-by-step approach and use the given information.

Given:
Width of the rectangle = X centimeters
Perimeter of the rectangle = 8X centimeters
Side length of the square = 1/4 * length of the rectangle

A) Finding the length of the rectangle:
Since a rectangle has opposite sides of equal length, the length of the rectangle is also X centimeters.

B) Finding the perimeter of the square:
The side length of the square is 1/4 times the length of the rectangle. So, the side length of the square = (1/4) * X centimeters.
Therefore, the perimeter of the square = 4 * side length = 4 * (1/4) * X = X centimeters.

C) Finding how many centimeters greater the rectangle is than the square's perimeter if X = 4:
Given X = 4, we substitute it into the formula to find the difference:
Difference = Perimeter of the rectangle - Perimeter of the square
Difference = 8X - X
Difference = 7X
Substituting X = 4 into the equation, we get:
Difference = 7 * 4 = 28 centimeters

D) Finding how many square centimeters greater the rectangle's area is than the square's area if X = 4:
Area of the rectangle = Length * Width = X * X
Area of the square = Side length * Side length = (1/4 * X) * (1/4 * X)
Difference in areas = Area of the rectangle - Area of the square
Difference in areas = (X * X) - ((1/4 * X) * (1/4 * X))
To simplify the expression, we substitute X = 4 into the equation:
Difference in areas = (4 * 4) - ((1/4 * 4) * (1/4 * 4))
Difference in areas = 16 - 1
Difference in areas = 15 square centimeters.

Therefore:
A) The length of the rectangle is X centimeters.
B) The perimeter of the square is X centimeters.
C) The rectangle is 28 centimeters greater than the square's perimeter when X = 4.
D) The rectangle's area is 15 square centimeters greater than the square's area when X = 4.

Please do not use all caps. Not only is it harder to read, but it is like SHOUTING online. Thank you.

Since there are two sides the same in the rectangle,

A. 2x +2( ?x) = 8x

B. 4(1/4x) = ?

I'll let you calculate the rest.