SOLUTION: A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower be

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower be      Log On


   

Question 248100: A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower bed?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width.
The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower
:
Let x = the width of flower bed
:
Then the overall dimensions (flower bed & lawn) will be:
(2x + 8) by (2x + 4)
:
Overall area
(2x+8)*(2x+4) = 165
FOIL
4x^2 + 8x + 16x + 32 = 165
A quadratic equation
4x^2 + 24x + 32 - 165 = 0
4x^2 + 24x - 132 = 0
Simplify, divide by 4, results:
x^2 + 6x - 33 = 0
Use the quadratic formula to solve this
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem: a=1; b=6; c=-33
x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A-33+%29%29%2F%282%2A1%29+
Do the math here and you should get a positive solutions of:
x ~ 3.48 meters is the width of the flower bed
;
:
Check on a calc: enter (2(3.48)+8)*(2(3.48)+4) = 164 ~ 165