| The area of a rectangle increases by 76 sq units, if the length and breadth is increased by 2 units. However, if the length is increased by |
| 3 units and breadth is decreased by |
| 3 units, the area of sets reduced by |
| 21 sq units. Find the breadth of the rectangle. |
A) 9 units
B) 16 units
C) 18 units
D) 21 units
Correct Answer: B
Solution :
| Let the length of the rectangle be x units and the breadth y units. |
| Then, \[\left( x+2 \right)\left( y+2 \right)=xy+76\] |
| \[\Rightarrow \,\,\,2x+2y+4=76\] |
| \[\Rightarrow \,\,\,\,x+y=36\] ...(i) |
| In the second case |
| \[\left( x+3 \right)\left( y-3 \right)=xy-21\] |
| \[\Rightarrow \,\,\,\,3y-3x-9=-21\] |
| \[\Rightarrow \,\,\,\,3x-3y=21-9=12\] |
| \[\Rightarrow \,\,\,\,x-y=4\] ...(ii) |
| From Eq. (i), |
| \[y\text{ }=\text{ }36\text{ }-\text{ }x\] |
| Substituting the value of y in Eq. (ii), we get |
| \[x-\left( 36-x \right)=4\] |
| \[\Rightarrow \,\,\,\,x-36+x=4\] |
| \[\Rightarrow \,\,\,\,2x=40\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,x=20\]units |
| And \[y=36-20=16\]units |
| Hence, length = 20 units |
| and breadth = 16 units |
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