The perimeter of a rectangle is equal to 4040. if the length is halved and the width is divided by 3, the new perimeter is decreased by 2424. what is the length of the original rectangle?

New perimeter is 4040-2424 = 1616

original, let x and y be length and width

2x + 2y = 4040

new

2x/2 + 2y/3 = 1616

x + 2y/3 = 1616

x = 1616 - 2y/3

sub this x value into first eq

2 (1616-2y/3) + 2y = 4040

3232 - 4y/3 + 2 = 4040

put like terms together

-4y/3+2y=4040-3232

2y/3=808

multiply both sides by 3

2y = 2424

divide both sides by 2

y=1212

sub this y value into any eq. i chose eq 1

2x+2 (1212) = 4040

2x = 4040 - 2 (1212)

2x = 1616

x = 808

so the length is 808 and the width is 1212