Question

The area of rectangle gets reduced by 80 sq.units and length reduced by 5 units breadth increased by 2 units if we increase length by 10 units and decrease breadth by 5 units then area will be increase by 50 units.Find length and breadth of rectangle.

Answer 1

Let the original length of rectangle = l unit
original breadth of rectangle = b unit
So, original area = lb sq units
A. New length = l - 5 and new breadth = b + 2
$\Rightarrow$ New area = (l - 5)(b + 2) = lb- 80
lb - 5b + 2l -10 = lb - 80
2l - 5b = - 70 or 5b - 2l = 70 ...(i)
B. New legnth = l + 10 ; new breadth = b - 5
$\Rightarrow$ New area = (l + 10)(b - 5) = lb + 50
lb + 10b - 5l - 50 = lb + 50
10b - 5l = 100 ...(ii)
Solving simultaneous equations (i) and (ii) :
From eq(1)$\times 2-$eq (2)
2(5b - 2l) - (10b - 5l) = 2 $\times$ 70 - 100
$\Rightarrow 10b-4l-10b+5l=140-100$
$\therefore l=40$ units.
Substittue $l=40$ in equation(i), we get
$\Rightarrow 5b-2\left(40\right)=70$
$5b-80=70$
$5b=150$
$\therefore b=30$ units.
Hence, l = 40 and b = 30 units.