Expert: Sherman D. - 8/29/2008

Question
QUESTION: A lumber company owns a forest that is of rectangle shape, 1 mi by 2mi.IF the company cuts a uniform strip of trees along the outer edges of this forest, how wide should the strip be if ¾ sq mi of forest is to remain

ANSWER: 1 * 2 * 3/4 = 6/4 = 3/2, so 1.5 sq. miles must remain.

if you cut a uniform strip to all outer edges, then your taking twice that length from the width and the length.

(1 - 2x)(2 - 2x) = (3/2)

Of your wondering about what i did, its just to find the area.

2 - 2x - 4x + 4x^2 = (3/2)
4x^2 - 6x + 2 = (3/2)
8x^2 - 12x + 4 = 3
8x^2 - 12x + 1 = 0


Using the quadratic formula

x = (-b ± sqrt(b^2 - 4ac))/(2a)

x = (-(-12) ± sqrt((-12)^2 - 4(8)(1)))/(2(8))
x = (12 ± sqrt(144 - 32))/16
x = (12 ± sqrt(112))/16
x = (12 ± sqrt(16 * 7))/16
x = (12 ± 4sqrt(7))/16
x = (1/4)(3 ± sqrt(7))

x = about .08856 or 1.4114

Since 1.4114 will give you a negative length and we can't have that

Plug .08856 in for x and you get

Width = .823 miles
Length = 1.823 miles

If i did this one correctly, that was what i got.

---------- FOLLOW-UP ----------

QUESTION:   A company parking lot is 120ft long and 80ft wide .due to a increase in personnel ,it is decided to double the area of the lot by adding strips of equal width to one end and one side.Find the width of one such strip?

Answer
120 * 80 = 9600

9600 * 2 = 19200

Since they are only doing it to one side and one end, they aren't doing it to both sides and both ends, so they are only adding an extra strip vertically and horizontally.

(120 + x)(80 + x) = 19200
9600 + 120x + 80x + x^2 = 19200
x^2 + 200x - 9600 = x

x = (-200 ± sqrt(200^2 - 4(-9600)(1)))/(2(1))
x = (-200 ± sqrt(40000 + 38400))/2
x = (-200 ± sqrt(78400))/2
x = (-200 ± 280))/2
x = (80/2) or (-480/2)

since you can't have a negative value.

x = 40

ANS : 40ft