SOLUTION: The state of Colorado is almost perfectly rectangular, with its north border 111 mi longer than its west border. If the state encompasses 104,000 mi^2, estimate the dimensions of C

Question 200551This question is from textbook Intermediate Algebra An Applied Approach
: The state of Colorado is almost perfectly rectangular, with its north border 111 mi longer than its west border. If the state encompasses 104,000 mi^2, estimate the dimensions of Colorado. Round to the nearest mile. This question is from textbook Intermediate Algebra An Applied Approach

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Area = Length * Width
.
104,000 = (w+111) * (w)= w^2 +111w
.
w^2 +111w -104,000 =0
.
Use quadratic eqn to solve
.
a=(1),,,,b=(111),,,,,c= (-104,000)
.
w= [ -(111) +/- sqrt { (111)^2 - 4 (1) (-104,000) } ] / 2 (1)
.
w = [-111 +/- sqrt 428,321 ] /2
.
w = [-111 +/- 654.642 ] /2
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w= 271.73 ,,,,,or - 382.73 ( not realistic)
.
Dimensions are ,,,w= 271.73,,,and L= 271.73 +111 = 382.73
.
check,,,A= 271.73 * 382.73 = 104,000,,,ok
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