Answer:
The dimensions of rectangle are
Length: 15 meters
Breadth: 12 meters
Step-by-step explanation:
Let
x ----> the original length of rectangle
y ---> the original breadth of rectangle
The area of rectangle is
[tex]A=xy[/tex]
1) The area of a rectangle reduces by 20 m2, if its length is increased by I m and the breadth is reduced by 2 m
[tex]A-20=(x+1)(y-2)[/tex]
[tex]A=(x+1)(y-2)+20[/tex]
[tex]A=xy-2x+y-2+20[/tex]
[tex]A=xy-2x+y+18[/tex]
Remember that
[tex]A=xy[/tex]
substitute
[tex]xy=xy-2x+y+18[/tex]
[tex]y=2x-18[/tex] -----> equation A
2) The area increases by 12 m², if the length is reduced by 3 m and the breadth is increased by 4 m.
[tex]A+12=(x-3)(y+4)[/tex]
[tex]A=(x-3)(y+4)-12[/tex]
[tex]A=xy+4x-3y-12-12[/tex]
[tex]A=xy+4x-3y-24[/tex]
Remember that
[tex]A=xy[/tex]
substitute
[tex]xy=xy+4x-3y-24[/tex]
[tex]4x-3y=24[/tex] -----> equation B
Solve the system of equations A and B by substitution
substitute equation A in equation B
[tex]4x-3(2x-18)=24[/tex]
solve for x
[tex]4x-6x+54=24\\2x=30\\x=15\ m[/tex]
Find the value of y
[tex]y=2(15)-18=12\ m[/tex]
therefore
The dimensions of rectangle are
Length: 15 meters
Breadth: 12 meters
