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The area of a rectangle gets reduced by 9 m2 if its length is reduced by 5 m and breath is increased by 3 m. If we increased the length by 3 m and breath by 2 m, the area is increased by 67 m2. The length of the rectangle is:
- a)9 m
- b)15.6 m
- c)17 m
- d)18.5 m
- e)19 m
Correct answer is option 'A,C'. Can you explain this answer?
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Verified Answer
The area of a rectangle gets reduced by 9 m2 if its length is reduced ...
Let length of rectangle = x units
And width of rectangle = y units
Area of rectangle = length * width = x*y
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.
So
Decrease the length by 5 unit so new length = x - 5
Increase the width by 3 unit so new width = y + 3
New area is reduced by 9 units
So new area = xy – 9
Plug the value in formula length * width = area we get
(x - 5)(y + 3) = xy - 9
Xy + 3x – 5y – 15 = xy – 9
Subtract xy both side we get
3x - 5y = 6 …(1)
If we increase the length by 3units and the breadth by 2 units, the area increases by 67 square units.
Increase the length by 3 unit so new length = x +3
Increase the width by 2 unit so new width = y + 2
New area is increased by 67 units
So new area = xy + 67
Plug the value in formula length * width = area we get
(x +3)(y + 2) = xy + 67
Xy + 2x + 3y + 6 = xy + 67
Subtract xy both side we get
2x + 3y = 61 …(2)*3
3x - 5y = 6 …(1)*2
Cross multiply the coefficient of x we get
6x + 9 y = 183
6x -10y =12
Subtract now we get
19 y = 171
Y = 171/19 = 9
Plug this value of y in equation first we get
2x + 3* 9 = 61
2x = 61 – 27
2x = 34
X = 34/2 = 17
So length is 17 units and width is 9 units
Most Upvoted Answer
The area of a rectangle gets reduced by 9 m2 if its length is reduced ...
Understanding the Problem
To find the length of the rectangle, we will set up equations based on the information provided.
Let Variables Represent Dimensions
- Let the original length be \( L \)
- Let the original breadth be \( B \)
Formulating the Equations
1. First Condition: Area Reduction
- The area decreases by 9 m² when:
- Length is reduced by 5 m: \( L - 5 \)
- Breadth is increased by 3 m: \( B + 3 \)
- The equation becomes:
\[
(L - 5)(B + 3) = LB - 9
\]
Simplifying gives:
\[
LB + 3L - 5B - 15 = LB - 9
\]
This reduces to:
\[
3L - 5B = 6 \quad (1)
\]
2. Second Condition: Area Increase
- The area increases by 67 m² when:
- Length is increased by 3 m: \( L + 3 \)
- Breadth is increased by 2 m: \( B + 2 \)
- The equation becomes:
\[
(L + 3)(B + 2) = LB + 67
\]
Simplifying gives:
\[
LB + 2L + 3B + 6 = LB + 67
\]
This reduces to:
\[
2L + 3B = 61 \quad (2)
\]
Solving the Equations
Now we have a system of linear equations:
- From equation (1): \( 3L - 5B = 6 \)
- From equation (2): \( 2L + 3B = 61 \)
To solve for \( L \) and \( B \), we can multiply equation (1) by 3 and equation (2) by 5:
- \( 9L - 15B = 18 \)
- \( 10L + 15B = 305 \)
Adding these gives:
\[
19L = 323 \implies L = 17
\]
Conclusion
Thus, the length of the rectangle is 17 m. The correct options are 'C'.
To find the length of the rectangle, we will set up equations based on the information provided.
Let Variables Represent Dimensions
- Let the original length be \( L \)
- Let the original breadth be \( B \)
Formulating the Equations
1. First Condition: Area Reduction
- The area decreases by 9 m² when:
- Length is reduced by 5 m: \( L - 5 \)
- Breadth is increased by 3 m: \( B + 3 \)
- The equation becomes:
\[
(L - 5)(B + 3) = LB - 9
\]
Simplifying gives:
\[
LB + 3L - 5B - 15 = LB - 9
\]
This reduces to:
\[
3L - 5B = 6 \quad (1)
\]
2. Second Condition: Area Increase
- The area increases by 67 m² when:
- Length is increased by 3 m: \( L + 3 \)
- Breadth is increased by 2 m: \( B + 2 \)
- The equation becomes:
\[
(L + 3)(B + 2) = LB + 67
\]
Simplifying gives:
\[
LB + 2L + 3B + 6 = LB + 67
\]
This reduces to:
\[
2L + 3B = 61 \quad (2)
\]
Solving the Equations
Now we have a system of linear equations:
- From equation (1): \( 3L - 5B = 6 \)
- From equation (2): \( 2L + 3B = 61 \)
To solve for \( L \) and \( B \), we can multiply equation (1) by 3 and equation (2) by 5:
- \( 9L - 15B = 18 \)
- \( 10L + 15B = 305 \)
Adding these gives:
\[
19L = 323 \implies L = 17
\]
Conclusion
Thus, the length of the rectangle is 17 m. The correct options are 'C'.
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The area of a rectangle gets reduced by 9 m2 if its length is reduced by 5 m and breath is increased by 3 m. If we increased the length by 3 m and breath by 2 m, the area is increased by 67 m2. The length of the rectangle is:a)9 mb)15.6 mc)17 md)18.5 me)19 mCorrect answer is option 'A,C'. Can you explain this answer?
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