Let the width of the original rectangle be W, then the length = (W + 5)

The area of this rectangle = W(W + 5) = W

The modified rectangle has a length 2(W + 5) and a width (W - 2)

The area of the modified rectangle = 2(W + 5)(W - 2) = 2W

As this area is 162 sq in greater than the original rectangle then we can write :-

2W

W

The can be factored

(W +14)(W - 13) = 0

We are only concerned with the positive root that occurs when (W - 13) = 0, thus W = 13

The dimensions of the original rectangle are Width 13 in, Length 18 in (W + 5)

The dimensions of the modified rectangle are Width 11 in (W - 2) and Length 36 in [(2(W + 5)]

The area of this rectangle = W(W + 5) = W

^{2}+5WThe modified rectangle has a length 2(W + 5) and a width (W - 2)

The area of the modified rectangle = 2(W + 5)(W - 2) = 2W

^{2}+ 6W - 20As this area is 162 sq in greater than the original rectangle then we can write :-

2W

^{2}+ 6W - 20 = W^{2}+ 5W + 162W

^{2 }+ W - 182 = 0The can be factored

(W +14)(W - 13) = 0

We are only concerned with the positive root that occurs when (W - 13) = 0, thus W = 13

The dimensions of the original rectangle are Width 13 in, Length 18 in (W + 5)

The dimensions of the modified rectangle are Width 11 in (W - 2) and Length 36 in [(2(W + 5)]