The length of a rectangular lot is 7 yards less than twice its width. If the length was increased by 11 yards and the width decreased by 6 yards, the area would be decreased by 40 square yards. Find the original dimension of the lot.
Accepted Solution
A:
Answer:The width = 16 yards and the length = 25 yards.Step-by-step explanation:Let x yards be the original width, then the original length is 2x - 7 yards.Therefore the original area = x(2x - 7) yd^2.The new area = (2x - 7 + 11)(x - 6) = (2x + 4)(x - 6) yd^2.So we have the equationx(2x - 7) - (2x + 4)(x - 6) = 402x^2 - 7x - (2x^2 - 12x + 4x - 24) = 402x^2 - 7x - 2x^2 + 8x + 24 - 40 = 0x - 16 = 0x = 16 yards = the width.The length = 2(16) - 7 = 25 yards.