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Lumber company owns forest 1 mile by 2 miles

A lumber company owns a forest that is rectangular in shape, 1 mile by 2 miles. If the company cuts a uniform strip of trees along all four outer edges of this forest, how wide should the strip be if 3/4 square mile of forest is to remain?
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2 Answers

x = length of inner rectangle
y = width of inner rectangle
w = width of strip
 
xy = 3/4 sq mi
 
x + 2w = 2 mi ==> x = 2 - 2w
y + 2w = 1 mi ==> y = 1 - 2w
 
(2 - 2w)(1 - 2w) = 3/4
(1 - w)(1 - 2w) = 3/8
1 - 2w - w + 2w^2 = 3/8
2w^2 - 3w + 1 = 3/8
16w^2 - 24w + 8 = 3
16w^2 - 24w + 5 = 0
(4w-1)(4w-5) = 0
 
w = 1/4 or w = 5/4
 
x = 2 - 2w
= 2 - 2(1/4) = 3/2 or
= 2 - 2(5/4) = –1/2
 
But x > 0 means w = 1/4 mi.
 
check:
 
(2 - 2(1/4))(1 - 2(1/4)) =? 3/4
(2 - 1/2)(1 - 1/2) =? 3/4
(3/2)(1/2) =? 3/4
3/4 = 3/4 √