SOLUTION: 30A garden area is 30 feet long qand 20 feet wide. A path of uniform width is set around the edge. If the remaining garden is 400 square feet, what is the width of the path? 30

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: 30A garden area is 30 feet long qand 20 feet wide. A path of uniform width is set around the edge. If the remaining garden is 400 square feet, what is the width of the path? 30       Log On

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Question 75093This question is from textbook Beginning Algebra
: 30A garden area is 30 feet long qand 20 feet wide. A path of uniform width is set around the edge. If the remaining garden is 400 square feet, what is the width of the path?
30 * 20 = 600
600-400 =200
lw=Area
lw= 200
I drew a picture and still really did not make sense. If I could figure out how to use the quadratic to solve this I could easily do the actual math, but I am struggling setting up the equation.This question is from textbook Beginning Algebra

Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
(30-2x)(20-2x)=400 the 2x is the width of the path (one at each end of the 20 & 30 foot outer measurements)
600-40x-60x+4x^2=400
4x^2-100x+600-400=0
4x^2-100x+200=0
x^2-25x+50
using the quadratic equation we get:
X=(25+-SQRT[25^2-4*1*50])/2*1
X=(25+-SQRT[625-200])/2
X=(25+-SQRT425)/2
X=(25+-20.6)/2
X=(25+20.6)/2
X=45.6/2
X=22.8 NOT AN ANSWER
X=(25-20.6)/2
X=4.4/2
X=2.2 ANSWER.
PROOF
(30-2*2.2)(20-2*2.2)=400
(30-4.4)(20-4.4)=400
25.6*15.6=400
400=400