SOLUTION: A gardener makes a rectangular flower bed square by taking two feet off its length and adding three feet to its breath. By doing so he increases the area by 20 square feet. What is
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Question 914364: A gardener makes a rectangular flower bed square by taking two feet off its length and adding three feet to its breath. By doing so he increases the area by 20 square feet. What is its final area?
Answer by JoelSchwartz(130) (Show Source): You can put this solution on YOUR website!
A=lw
A=area of a rectangle
A+20=area of a square
s1=L-2
s2=w+3
A+20=(L-2)(w+3)
Lw+20=Lw-2w+3L-6
20=-2w+3L-6
26=-2w+3L
26+2w=3L
8+2/3+2/3w=L
w(8+2/3+2/3w)=A
8w+2/3w+2/3w^2=A
26/3w+2/3w^2=A
26/3w+2/3w^2+20=(w+3)(w+3)
26/3w+2/3w^2+20=w^2+3w+3w+9
26/3w+2/3w^2+20=w^2+6w+9
26/3w-18/3w+11=w^2-2/3w^2
8/3w+11=1/3w^2
-1/3w^2+8/3w+11=0
-w^2+8w+33=0
(-w+11)(w+3)=0
-w+11=0
-w=-11
w=11
A+20=(w+3)^2
A+20=14^2
A+20=196
A=176
The final area of the square is 196 square feet.
The area of the rectangle is 176 square feet.
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