- ) 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
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.
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
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