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The area of a rectangle gets reduced by 9 square units,if its length is reduced by 5 units and breadth is increased by 3 units.If we increase the length by 3 units and breadth by 2 units, then the area is increased by 67 square units. Find the length and breadth of the rectangle.
- a)15m, 9m
- b)17m, 9m
- c)14m, 7m
- d)16m, 7m
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The area of a rectangle gets reduced by 9 square units,if its length i...
Length = x; Breadth =y
xy – (x-5)(y+3) = 9
3x – 5y – 6 = 0 —(i)
(x+3)(y+2) – xy = 67
2x + 3y -61 = 0 —(ii)
solving (i) and (ii)
x = 17m ; y = 9m
xy – (x-5)(y+3) = 9
3x – 5y – 6 = 0 —(i)
(x+3)(y+2) – xy = 67
2x + 3y -61 = 0 —(ii)
solving (i) and (ii)
x = 17m ; y = 9m
Most Upvoted Answer
The area of a rectangle gets reduced by 9 square units,if its length i...
To solve this problem, we need to use the formula for the area of a rectangle, which is length multiplied by breadth.
Let's denote the original length of the rectangle as L and the original breadth as B.
First, we are given that the area of the rectangle is reduced by 9 square units when the length is reduced by 5 units and the breadth is increased by 3 units. This can be expressed as:
(L - 5)(B + 3) = LB - 9
Next, we are given that when the length is increased by 3 units and the breadth is increased by 2 units, the area is increased by 67 square units. This can be expressed as:
(L + 3)(B + 2) = LB + 67
Now, we have two equations with two variables. Let's solve them simultaneously to find the values of L and B.
Expanding the first equation, we get:
LB - 5B + 3L - 15 = LB - 9
Simplifying and rearranging the terms, we have:
3L - 5B = -6 ----(1)
Expanding the second equation, we get:
LB + 3B + 2L + 6 = LB + 67
Simplifying and rearranging the terms, we have:
2L + 3B = 61 ----(2)
Now, we can solve equations (1) and (2) simultaneously to find the values of L and B.
Multiplying equation (1) by 2 and equation (2) by 3, we get:
6L - 10B = -12 ----(3)
6L + 9B = 183 ----(4)
Subtracting equation (3) from equation (4), we eliminate the variable L:
19B = 195
Dividing both sides of the equation by 19, we get:
B = 10.26
Since the length and breadth of a rectangle cannot be decimal values, we round B to the nearest whole number, which is 10.
Substituting the value of B back into equation (1), we can solve for L:
3L - 5(10) = -6
3L - 50 = -6
3L = 44
L = 14.67
Again, rounding L to the nearest whole number, we get L = 15.
Therefore, the length of the rectangle is 15 units and the breadth is 10 units.
The correct answer is option B: 15m, 10m.
Let's denote the original length of the rectangle as L and the original breadth as B.
First, we are given that the area of the rectangle is reduced by 9 square units when the length is reduced by 5 units and the breadth is increased by 3 units. This can be expressed as:
(L - 5)(B + 3) = LB - 9
Next, we are given that when the length is increased by 3 units and the breadth is increased by 2 units, the area is increased by 67 square units. This can be expressed as:
(L + 3)(B + 2) = LB + 67
Now, we have two equations with two variables. Let's solve them simultaneously to find the values of L and B.
Expanding the first equation, we get:
LB - 5B + 3L - 15 = LB - 9
Simplifying and rearranging the terms, we have:
3L - 5B = -6 ----(1)
Expanding the second equation, we get:
LB + 3B + 2L + 6 = LB + 67
Simplifying and rearranging the terms, we have:
2L + 3B = 61 ----(2)
Now, we can solve equations (1) and (2) simultaneously to find the values of L and B.
Multiplying equation (1) by 2 and equation (2) by 3, we get:
6L - 10B = -12 ----(3)
6L + 9B = 183 ----(4)
Subtracting equation (3) from equation (4), we eliminate the variable L:
19B = 195
Dividing both sides of the equation by 19, we get:
B = 10.26
Since the length and breadth of a rectangle cannot be decimal values, we round B to the nearest whole number, which is 10.
Substituting the value of B back into equation (1), we can solve for L:
3L - 5(10) = -6
3L - 50 = -6
3L = 44
L = 14.67
Again, rounding L to the nearest whole number, we get L = 15.
Therefore, the length of the rectangle is 15 units and the breadth is 10 units.
The correct answer is option B: 15m, 10m.
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