Question

The area of a rectangle gets reduced by $9$ square units if its length is reduced by $5$ units and the breadth is increased by $3$ units. If we increase the length by $3$ units and breadth by $2$ units, the area is increased by $67$ square units. Find the length and breadth of the rectangle.

• A. Length $=22$ units breadth $=6$ units
• B. Length $=28$ units breadth $=13$ units
• C. Length $=15$ units breadth $=8$ units
• D. Length $=17$ units breadth $=9$ units

Answer 1

Answer: (D)

Length $=17$ units breadth $=9$ units

Let the length of the rectangle $=x$ units

The breadth of the rectangle $=y$ units

$\therefore$ Area of rectangle $=xy$ sq. units

According to the first condition

$\Rightarrow (x-5)(y+3)=xy-9$

$\Rightarrow xy+3x-5y-15=xy-9$

$\Rightarrow 3x-5y=\mathrm{6........}eq1$

According to the second condition

$\Rightarrow (x+3)(y+2)=xy+67$

$\Rightarrow xy+2x+3y+6=xy+67$

$\Rightarrow 2x+3y=\mathrm{61.....}eq2$

Multiply eq1 by 3 and eq2 by 5

$\Rightarrow 9x-15y=\mathrm{18.......}eq3$

$\Rightarrow 10x+15y=\mathrm{305........}eq4$

Adding $eq3$ and $eq4$

$\Rightarrow 19x=323\Rightarrow x=17$

Put $x=17$ in $eq2$

$\Rightarrow 2\times 14+3y=61$

$\Rightarrow 3y=27\Rightarrow y=9$

Hence, the length of the rectangle $=17$ units

The breadth of the rectangle $=9$ units