Question

URGENT!! YOU WILL GET BRAINLIEST!

Answer 1

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