Question

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. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle. [4 MARKS]

Answer 1

Formula: 1 Mark
Concept: 1 Mark
Application: 2 Marks

Let length be $l$ & breadth be $b$

Area of rectangle is $=length\times breadth$

According to given condition,

$(l-5)(b+3)=lb-9$

$\Rightarrow lb-5b+3l-15=lb–9$

$\Rightarrow 3l-5b=6\dots \dots \left(i\right)$

Also,

$(l+3)(b+2)=lb+67$

$2l+3b=61\dots \dots \left(ii\right)$

Solving (i) and (ii) we get,

$2\times \left(i\right)-3\times \left(ii\right)\Rightarrow$

$6l-10b-6l-9b=12-183$

$-19b=-171\Rightarrow b=9$

Substituting value of b in (i)

$3l-5\left(9\right)=6\Rightarrow l=17$

$\Rightarrow l=17,b=9$

$\therefore$ The length is 17 units and breadth is 9 units.