Question

the dimensions of a rectangular field are 50m and 40m. S flower bed is prepared inside this field leaving a gravel path of uniform width all around the flower bed. The total cost of laying the flower bed and the gravelling the path at rs30 and rs20 per square metre, respectively, is rs52000. Find the width of gravel path.​

Answer 1

$\huge\bold{\mathtt{\purple{ A{\pink{ N{\green{ S{\blue{ W{\red{ E{\orange{ R}}}}}}}}}}}}}$

Given,

dimensions of rectangular field =50m×40m

cost of flowering bed = 30Rs/m 2

cost of grovelling path = 20Rs/m 2

Let width of gravel =x m

area of field = 50×40=2000m 2

area of flower bed = (50−2x)(40−2x)

Total cost

= cost of flower bed+ grovelling path

∴52000=[(50−2x)(40−2x)×30] +[(2×50×x)+2(40−2x)x]×20

=52000=[(2000−100x−80x+4x 2 )×30] +[100x+80−4x 2 ]×20

=52000=60000−5400x+120x 2+3600x−8x 2

=40x 2 −1800x+8000=0

=x 2 −45x+200=0∴

x=5,40

40 can't be the value of x as

it is the total field width

∴x=5m

Thus, gravel path width is 5m

PLEASE MARK ME AS BRAINLIEST IF IT WAS HELPFUL