The original length L is 40 units, and the original breadth B is 34 units.
Let's denote the original length of the rectangle as L and the original breadth as B. The area of the rectangle is given by
A=L×B.
According to the problem:
When the length is reduced by 5 units and the breadth is increased by 2 units:
(L−5)×(B+2)=A−80
When the length is increased by 10 units and the breadth is decreased by 5 units:
(L+10)×(B−5)=A+50
We can set up a system of two equations using these conditions:
(L−5)×(B+2)=A−80
(L+10)×(B−5)=A+50
Now, let's expand these equations:
LB+2L−5B−10=A−80
LB−5L+10B−50=A+50
Now, substitute A=LB into both equations:
LB+2L−5B−10=LB−80
LB−5L+10B−50=LB+50
Simplify the equations:
2L−5B−10=−80
−5L+10B−50=50
Now, let's solve this system of equations. We can multiply the first equation by 2 to make the coefficients of L in both equations equal:
4L−10B−20=−160
−5L+10B−50=50
Add the two equations:
(−L−70=−110)
Now, solve for L:
L=40
Now, substitute L=40 into one of the original equations, for example, the first one:
2(40)−5B−10=−80
80−5B−10=−80
−5B=−170
B=34
So, the original length L is 40 units, and the original breadth B is 34 units.