Let Xo = original length of the deck Yo = original width of deck Therefore: Yo = (1/6)Xo The original deck area is: Ao = XoYo Ao = Xo(1/6)Xo = (1/6)Xo2 The length of the new deck is 4ft longer than the original deck, or XN = Xo + 4, and the width is 2ft longer than the original, or YN = Yo + 2, and the new area of the deck is 56ft2 than the original area, or AN = Ao + 56. Therefore: AN = XNYN Ao + 56 = (Xo + 4)(Yo + 2) (1/6)Xo2 + 56 = (Xo + 4)(1/6Xo + 2) (1/6)Xo2 + 56 = (1/6)Xo2 + 2Xo + (4/6)Xo +8 56 = 2Xo + (2/3)Xo +8 56 - 8 = (2 + 2/3)Xo 48 = (6/3 + 2/3)Xo 48 = (8/3)Xo 48(3/8) = Xo Xo = 18ft Yo = (1/6)(18) Yo = 3ft Check: Ao = XoYo = (18)(3) = 54ft2 XN = Xo + 4 = 18 + 4 = 22ft YN = Yo + 2 = 3 + 2 = 5ft AN = (22)(5) = 110ft2 Ao + 56 = AN 54 + 56 = 110 110 = 110 check------->ANSWER: original length, Xo = 18ft original width, Yo = 3ft
