SOLUTION: A gareen is currently 4 m wide and 7 m long. If the area of the garden is to be doubled by increasing the width and length by the same number of meters, find the new dimensions of

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Question 192101: A gareen is currently 4 m wide and 7 m long. If the area of the garden is to be doubled by increasing the width and length by the same number of meters, find the new dimensions of the garden.
Found 2 solutions by RAY100, checkley75:
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
Area = L*w
original Area = 4*7=28
new graden is (2) * (28)=56 (given)
new garden Area is (4+x) *(7+x) =56
using FOIL
28 +4x+7x+x^2 =56
28 +11x+x^2 =56
subt 56 both sides
28-56 +x^2+11x =0
x^2 +11x -28 =0
factoring will not work so use quadratic eqn
a=(1), b=(11), c=(-28)
x= ( -(11) +- ( (11)^2-4(1)(-28) ^.5) )/2(1)
x=( (-11) +- (15.26) )/2
x=( (-11) +15.26 )/2 = 2.13
or x= ( (-11) -15.26 ) /2 = -13.13 not realistic
check
a= (4+2.13) *(7+2.13) = 6.13*9.13 = 56 ok

answer is (6.13) by (9.13) m

Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
4*7=28 m^2 is the original area.
(4+x)(7+x)=2*28
28+11x+x^2=56
x^2+11x+28-56=0
x^2+11x-28=0

x=(-11+-sqrt[11^2-4*1*-28])/2*1
x=(-11+-sqrt[121+112])/2
x=(-11+-sqrt233)/2
x=(-11+-15.26)/2
x=(-11+15.26)2
x=4.264/2
x=2.132 meters is the increase needed to double the garden size.
Proof:
(4+2.132)(7+2.132)=56
6.132*9.132=56
56~56