Length of a rectangular field is increased by 10 meters and breadth is decreased by 4 meters, area of the field remains unchanged. If the length decreased by 5 meters and breadth is increased by 7 meters, again the area remains unchanged. Find the length and breadth of the rectangular field.a)12, 11b)13, 12c)13,11d)14,12e)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Length = l and breadth = b,
(l +10)*(b-4) = lb and (l-5)*(b+7) = lb
Solve both equation to get l and b

Answer

Length = l and breadth = b,
(l +10)*(b-4) = lb and (l-5)*(b+7) = lb
Solve both equation to get l and b

Answer

Length = l and breadth = b,
(l +10)*(b-4) = lb and (l-5)*(b+7) = lb
Solve both equation to get l and b

Answer

Let's assume the initial length of the rectangular field is L meters and the initial breadth is B meters.

First condition:
According to the given condition, when the length is increased by 10 meters and the breadth is decreased by 4 meters, the area of the field remains unchanged.

So, the new length becomes L + 10 meters and the new breadth becomes B - 4 meters.

The area of the field is given by the formula:
Area = Length * Breadth

Since the area remains unchanged, we can write the equation as:
L * B = (L + 10) * (B - 4)

Expanding the equation:
LB = LB + 10B - 4L - 40

Simplifying the equation:
10B - 4L = 40

Second condition:
According to the given condition, when the length is decreased by 5 meters and the breadth is increased by 7 meters, the area of the field remains unchanged.

So, the new length becomes L - 5 meters and the new breadth becomes B + 7 meters.

Using the same formula for area, we can write the equation as:
L * B = (L - 5) * (B + 7)

Expanding the equation:
LB = LB - 5B + 7L - 35

Simplifying the equation:
7L - 5B = 35

Solving the equations:
We now have two equations:
10B - 4L = 40
7L - 5B = 35

To solve these equations, we can multiply the first equation by 5 and the second equation by 4 to eliminate the variable B.

Multiplying the first equation by 5:
50B - 20L = 200

Multiplying the second equation by 4:
28L - 20B = 140

Adding the two equations:
50B - 20L + 28L - 20B = 200 + 140
30B + 8L = 340

Dividing the equation by 2:
15B + 4L = 170

Now we have two equations:
15B + 4L = 170
7L - 5B = 35

Solving these equations gives us:
L = 13 meters
B = 11 meters

Therefore, the length of the rectangular field is 13 meters and the breadth is 11 meters.

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