SOLUTION: A rectangular flower garden with dimensions 3m by 7m is surrounded by the walk of uniform width. If the area of the walk is 11 sq. m, what is the width in meters?

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Question 478749: A rectangular flower garden with dimensions 3m by 7m is surrounded by
the walk of uniform width. If the area of the walk is 11 sq. m, what is the
width in meters?
Found 2 solutions by mananth, cleomenius:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of sidewalk be x
Length of garden =7
Width = 3
Area = 21M^2
Area of sidewalk =11 M^2
Length of ground + sidewalk = 7+2x
width of ground + sidewalk = 3+2x

(7+2x)(3 +2x)-11 =21

21+14x+6 x+4x^2- 11=21
4x^2+20x -11=0
Find the roots of the equation by quadratic formula a= 4 b= 20 c= -11
b^2-4ac= 400 + 176
b^2-4ac= 576
sqrt%28%09576%09%29= 24
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( -20 + 24 )/ 8
x1= 0.5
x2=( -20 -24 ) / 8
x2= -5.5
Ignore negative value
The width = 0.5 m
m.ananth@hotmail.ca


Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
We have the area of the garden is 3 * 7 = 21 sq m., if the area of the walk is 11 the total area is 32 sq. m
(7 + x)(3 + x) = 32 sq. meters.
x^2 + 10x + 21 = 32
x*2 + 10x -11 = 0
(x + 11)(x - 1) = 0
x = 1
To check, 4 * 8 = 32 sq m.
We can see this does check.
Cleomenius.