Question

Show all the work and answer quick!

Answer 1

a) 3x

b) 3x

c) 2 2/3 times greater

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)

`(1)/(4) ((3x)/(1) )` =
`(3)/(4) x`

Now find the perimeter of the square by multiplying the side length by 4.

`(3)/(4)x((4)/(1) )` =
`3x`

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.