SOLUTION: A uniform-width boardwalk is built around the inside edge of a rectangular parkland that is 10m by 15m. If the boardwalk takes 20% of the lot, how wide is the boardwalk to the near

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: A uniform-width boardwalk is built around the inside edge of a rectangular parkland that is 10m by 15m. If the boardwalk takes 20% of the lot, how wide is the boardwalk to the near      Log On


   

Question 288985: A uniform-width boardwalk is built around the inside edge of a rectangular parkland that is 10m by 15m. If the boardwalk takes 20% of the lot, how wide is the boardwalk to the nearest centimetre?
Answer by mananth(16946) About Me  (Show Source):
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A uniform-width boardwalk is built around the inside edge of a rectangular parkland that is 10m by 15m. If the boardwalk takes 20% of the lot, how wide is the boardwalk to the nearest centimetre?
The area of parkland = 10* 15 = 150 sq. meters
Boardwalk takes 20% of 150
=20/100 * 150
=30 sq. mtrs.
let the width of the boardwalk be x
the length of parkland excluding width of board walk = 15-2x
width will be 10-2x
150 - (15-2x)(10-2x)=30
150 -{ 150 -30x-20x+4x^2}=30
150-150+50x-4x^2-30=0
4x^2-50x-30=0
taking the roots of the equation
x1= 50+sqrt(2500+480) / 8
=50+sqrt2980 /8
=13.07 Or 13
x2 will be negative
so 13 meters is the width of the board walk