Question 1174393
let L = the length
let W = the width.
the perimeter of the lot is equal to 2 * (L + W)
the area of the lot is equal to L * W


you are given that the length of a rectangular lot is 14 meters less than twice the lot’s width.


the equation for that is:
L = 2W - 14


The owner decided to decrease the length and the width by 3 meters each for landscaping purposes. The perimeter of the smaller rectangular lot is 80 meters.


since perimeter = 2 * (L - 3 + W - 3), then your equation for this is:


80 = 2 * (L - 3 + W - 3)
combine like terms in this to get:
80 = 2 * (L + W - 6)
simplify further to get:
80 = 2L + 2W - 12


you were given that L = 2W - 14, therefore replace L with 2W - 14 in the equation of 80 = 2L + 2W - 12 to get:
80 = 2 * (2W - 14) + 2W - 12
simplify to get:
80 = 4W - 28 + 2W - 12
combine like terms to get:
80 = 6W - 40
add 40 to both sides of this equation to get:
120 = 6W
solve for W to get:
W = 120 / 6 = 20


since L = 2W - 14, then L = 40 - 14 = 26


you have L = 26 and W = 20


taking 3 off of each, you have:
L - 3 = 23
W - 3 = 17


the formula for the perimeter becomes 80 = 2 * (23 + 17) = 46 + 34 = 80.
this confirms the values for L and W are correct.


you want to know the area of the original lot.


that would be area = L * W = 26 * 20 = 520 square meters.