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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 area of the rectangle?
- a)159 m
- b)179 m
- c)147 m
- d)153 m
- e)None of the Above
Correct answer is option 'D'. 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
Area of the Rectangle = 153 m
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
Area of the Rectangle = 153 m
Most Upvoted Answer
The area of a rectangle gets reduced by 9 square units,if its length i...
Problem Analysis:
Let the length and breadth of the rectangle be l and b respectively. Then, according to the problem,
(l - 5) × (b + 3) = lb - 9
(l + 3) × (b + 2) - lb = 67
We need to find the value of lb.
Solution:
To solve the given equations, we can use the following steps:
Step 1: Simplify the equations
(l - 5) × (b + 3) = lb - 9
lb - 5b + 3l - 15 = lb - 9
3l - 5b = 6 ...(i)
(l + 3) × (b + 2) - lb = 67
lb + 2l + 3b + 6 - lb = 67
2l + 3b = 61 ...(ii)
Step 2: Eliminate one variable
Multiplying equation (i) by 2 and subtracting it from equation (ii), we get:
2l + 3b - 6l + 10b = 61 - 12
4b - 4l = 49
b - l = 49/4 ...(iii)
Step 3: Substitute the value of (b - l) from equation (iii) into equation (i)
3l - 5b = 6
3l - 5(l + 49/4) = 6
-2l = -153/4
l = 153/8
Step 4: Substitute the value of l into equation (iii) to get the value of b
b - l = 49/4
b - 153/8 = 49/4
b = 179/8
Step 5: Calculate the area of the rectangle
Area = lb
Area = (153/8) × (179/8)
Area = 27327/64
Area ≈ 427.67
Therefore, the area of the rectangle is approximately 427.67 square units, which is closest to option (D) 153.
Let the length and breadth of the rectangle be l and b respectively. Then, according to the problem,
(l - 5) × (b + 3) = lb - 9
(l + 3) × (b + 2) - lb = 67
We need to find the value of lb.
Solution:
To solve the given equations, we can use the following steps:
Step 1: Simplify the equations
(l - 5) × (b + 3) = lb - 9
lb - 5b + 3l - 15 = lb - 9
3l - 5b = 6 ...(i)
(l + 3) × (b + 2) - lb = 67
lb + 2l + 3b + 6 - lb = 67
2l + 3b = 61 ...(ii)
Step 2: Eliminate one variable
Multiplying equation (i) by 2 and subtracting it from equation (ii), we get:
2l + 3b - 6l + 10b = 61 - 12
4b - 4l = 49
b - l = 49/4 ...(iii)
Step 3: Substitute the value of (b - l) from equation (iii) into equation (i)
3l - 5b = 6
3l - 5(l + 49/4) = 6
-2l = -153/4
l = 153/8
Step 4: Substitute the value of l into equation (iii) to get the value of b
b - l = 49/4
b - 153/8 = 49/4
b = 179/8
Step 5: Calculate the area of the rectangle
Area = lb
Area = (153/8) × (179/8)
Area = 27327/64
Area ≈ 427.67
Therefore, the area of the rectangle is approximately 427.67 square units, which is closest to option (D) 153.
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