Lumber company owns forest 1 mile by 2 miles

Question

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?

Answer 1

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 √

Answer 2

Hope this helps:

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