SOLUTION: A rectangular field has dimesions 50 m by 40 m. A flowerbed is prepared inside the field with a gravel footpath of equal width around it. The cost of preparing the flowerbed and gr

Question 883351: A rectangular field has dimesions 50 m by 40 m. A flowerbed is prepared inside the field with a gravel footpath of equal width around it. The cost of preparing the flowerbed and gravel footpath is Rs.30 and Rs. 20 per sqm respectively amounting to Rs. 52000. Find the width of the footpath.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
A rectangular field has dimesions 50 m by 40 m.
Area of filed = 50*40 2000 m^2
Let width of footpath be x
Length of flower bed = (50-2x)
breadth of flower bed = (40-2x)
Area of flower bed = (50-2x)(40-2x)
cost of making flower bed = 30/m^2
Area of footpath = area of field - area of flower bed
Area of foot path = (2000-(50-2x)(40-2x))
cost of making foot path = 20/m^2
Total cost = 52000
30(50-2x)(40-2x) +20*(2000-(50-2x)(40-2x))=52000
30(2000-100x-80x+4x^2)+20(2000-(2000-100x-80x+4x^2))=52000
60000-5400x+120x^2+ 20(2000-2000+180x-4x^2)=52000
60000-5400x+120x^2+ 40000-40000+3600x-80x^2)=52000
60000-1800x+40x^2=52000
40x^2-1800x+8000=0
/10
4x^2-180x+800=0
4x^2-160x-20x+800=0
4x(x-40)-20(x-40)=0
(x-40)(4x-20)=0
x=40 OR x=5
it cannot be 40 m since width is 40 m
so width = 5 m
RELATED QUESTIONS
the dimension of a rectangular field are 50 m by 40 m. A flower bed is prepared inside... (answered by geetha_rama)

Please help me solving this question "A footpath a uniform width runs round the inside of (answered by rothauserc)

the area of square field is 5184 m. square. a rectangular field , whose length is twice... (answered by doukungfoo)

A rectangular field is 64 m X 25 m. Shawn wants to fence a square field that has the... (answered by checkley79)

the area of a rectangular field is 2275 . The field is enclosed by 200 m of fencing. What (answered by flame8855)

A rectangular field is 40 m longer than it is wide. The field is subdivided into 3 parts... (answered by ikleyn)

the diagonal of a rectangular field is 50 m and its breadth is 14 m .find its... (answered by MathLover1)

A rectangular field measures 30 m by 40 m. What is the length of the diagonal, x, from... (answered by mananth)

A field is 250 m by 310 m. A barn with floor dimensions of 21 m by 34 m is built in the... (answered by rfer)