The area of a rectangle gets reduced by 67 square meter , when it's length is increased by 3m and breadth is decreased by 4m. If length is reduced by 1m and breadth is increased by 4m, the area is increased by 89 square meter. Find the dimensions of the rectangle .?

Question

Answer

Answer

Answer

532 Sq. meter

Answer

Given information:
- The area of a rectangle is reduced by 67 square meters when the length is increased by 3 meters and the breadth is decreased by 4 meters.
- The area of the rectangle is increased by 89 square meters when the length is reduced by 1 meter and the breadth is increased by 4 meters.

Let's assume:
- Length of the rectangle = L meters
- Breadth of the rectangle = B meters

Calculating the area:
- The initial area of the rectangle = L * B square meters
- The area after the first change = (L + 3) * (B - 4) square meters
- The area after the second change = (L - 1) * (B + 4) square meters

Calculating the dimensions:
- According to the given information, the area of the rectangle is reduced by 67 square meters. So, we can write the equation:
L * B - (L + 3) * (B - 4) = 67

Expanding the equation:
L * B - (L * B - 4L + 3B - 12) = 67
L * B - L * B + 4L - 3B + 12 = 67
4L - 3B + 12 = 67

Rearranging the equation:
4L - 3B = 67 - 12
4L - 3B = 55

- According to the given information, the area of the rectangle is increased by 89 square meters. So, we can write the equation:
(L - 1) * (B + 4) - L * B = 89

Expanding the equation:
LB - B + 4L - 4 - LB = 89
B - 4L + 4 = 89

Rearranging the equation:
B - 4L = 89 - 4
B - 4L = 85

- We now have a system of equations:
4L - 3B = 55
B - 4L = 85

Solving the system of equations:
- We can solve this system of equations using the substitution method or the elimination method.

Substitution method:
- Rearrange the second equation to express B in terms of L:
B = 4L + 85

- Substitute the value of B in the first equation:
4L - 3(4L + 85) = 55

Simplify the equation:
4L - 12L - 255 = 55
-8L = 55 + 255
-8L = 310
L = 310 / -8
L = -38.75

- Substitute the value of L in the second equation:
B - 4(-38.75) = 85
B + 155 = 85
B = 85 - 155
B = -70

Conclusion:
- The dimensions of the rectangle cannot be negative as they represent physical measurements. Therefore, there is no valid solution

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