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

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) (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
RELATED QUESTIONS
Solve. A garden area is 30 feet long and 20 feet wide. A path of uniform width is set... (answered by jaymore)

Solve. A garden area is 30 feet long and 20 feet wide. A path of uniform width is set... (answered by ankor@dixie-net.com)

Solve. A garden area is 30 feet long and 20 feet wide. A path of uniform width is set... (answered by scott8148)

A garden area is 30 feet long and 20 feet wide. A path of uniform width is set around the (answered by Paul)

A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the... (answered by adamchapman)

Construction. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set... (answered by checkley71)

A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the... (answered by cathieb1225)

Construction. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set... (answered by ankor@dixie-net.com)