Answer:
a) 3x
b) 3x
c) 2 2/3 times greater
Step-by-step explanation:
The length of the rectangle:
The width of the rectangle is x. If you add the two widths together when finding perimeter, x + x, that would give you 2x.
Sum of widths: x + x = 2x
Use the sum of the widths to find the sum of the lengths by subtracting from the perimeter.
sum of lengths = perimeter - sum of widths
8x - 2x = 6x
Since there are 2 lengths divide by 2.
6x/2 = 3x
The length of the rectangle is 3x
Perimeter of the square:
The sides of the square are 1/4 of the length of the rectangle. "of" means to mulitply: (I made 3x a fraction by placing it over 1)
[tex]\frac{1}{4} (\frac{3x}{1} )[/tex] = [tex]\frac{3}{4} x[/tex]
Now find the perimeter of the square by multiplying the side length by 4.
[tex]\frac{3}{4}x(\frac{4}{1} )[/tex] = [tex]3x[/tex]
Last part:
solve the rectangle's perimeter by substituting x with 4.
P = 8x
P = 8(4)
P = 32 cm
Solve the square's perimeter by substituting x with 4.
P = 3x
P = 3(4)
P = 12 cm
Divide the rectangle's perimeter by the square's perimeter.
32/12 = 2 2/3 times bigger.
