Math, asked by rasviyasidik9, 22 days ago

- ) The length and breadth of a rectangular plot is (2x + 3) m and (3x - 4) m, respectively. (a) What will be the total cost of fencing the plot's boundary if the rate of fencing is 83x per metre? (b) If its length is increased by (x + 5) m and breadth is decreased by (x - 5) m, then find the difference between the area of the modified plot and that of the original plot​

Answers

Answered by lalithdv08
0

Answer:

The length and breadth of a rectangular plot is (2x+3) m and (3x - 4) m, respectively.

(a) What will be the total cost of fencing the plot's boundary if the rate of fencing is 23 per metre?

(b) If its length is increased by (x+5) m and its breadth is decreased by (x-5) m,

then find the difference between the area of the modified plot and that of the

original plot.

Answered by ChitranjanMahajan
0

The cost of fencing the boundary is 830x² - 166x units and the difference between the modified and original plot is  (18x + 20) m²

Given

  • The length and breadth of a rectangular plot are (2x + 3) m and (3x - 4) m, respectively.
  • The rate of fencing is 83x per meter
  • length is increased by (x + 5) m
  • breadth is decreased by (x - 5) m

To Find

  • Cost of fencing
  • The difference in the area of the modified and original plot

a)

Perimeter of a rectangle = 2(l + b)

where l and be are the length and breadth of the rectangle respectively

Therefore perimeter

= 2(2x + 3 + 3x - 4) m

= 2(5x - 1) m

= (10x - 2) m

Cost of fencing = rate of fencing per meter X perimeter

(10x - 2)83x  units

= 830x² - 166x units

b)

area of original plot lb

= (2x + 3)(3x - 4) m²

2x.3x + (2x)(-4) +3.3x + 3(-4) m²

= (6x² - 8x + 9x - 12  ) m²

=  (6x² + x - 12) m²

New length = (2x + 3 + x + 5) m

= (3x + 8 ) m

New breadth = 3x - 4 - (x - 5)

= (2x +1) m

New area = (3x + 8)(2x + 1) m²

= ( 6x² + 3x + 16x + 8) m²

=  (6x² + 19x + 8) m²

Therefore, the difference between the area of the modified and original plot is

(6x² + 19x + 8 - (6x² + x - 12)) m²

= (6x² + 19x + 8 - 6x² - x + 12) m²

= (18x + 20) m²

Hence, the cost of fencing the boundary is 830x² - 166x units and the difference between the modified and original plot is  (18x + 20) m²

#SPJ2

Similar questions