A rectangle has a width of x centimeters and a perimeter of

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 length of the rectangle. Find the length of the rectangle. Find the perimeter of the square. Find how many centimeters greater the rectangle\'s perimeter is than the square\'s perimeter if x = 4. Find how many square centimeters greater the rectangle\'s area is than the square\'s area if x = 4.

Solution

A.

For rectangular :

width = x cm

perimeter = 2*(w + L) = 8x cm

w+ L = 4x cm

length of rectangle:

L = 3x cm

B.

Length of square = 3x/4

perimeter of square = 4*(length) = 4*(3x/4)

perimeter = 3x cm

C.

when x = 4

rectangles perimeter = 2*(x + 3x) = 8*4 = 32 cm

square\'s perimeter = 3x = 3*4 = 12 cm

20 cm greater

D.

rectangle\'s area = x*3x = 3x^2 = 3*4^2 = 48 sq cm

square\'s area = (3x/4)^2 = (3*4/4)^2 = 9 sq cm

39 sq cm greater.