Question

POP

Answer 1

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

$A=xy$

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

$A-20=(x+1)(y-2)$

$A=(x+1)(y-2)+20$

$A=xy-2x+y-2+20$

$A=xy-2x+y+18$

Remember that

$A=xy$

substitute

$xy=xy-2x+y+18$

$y=2x-18$ -----> 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.

$A+12=(x-3)(y+4)$

$A=(x-3)(y+4)-12$

$A=xy+4x-3y-12-12$

$A=xy+4x-3y-24$

Remember that

$A=xy$

substitute

$xy=xy+4x-3y-24$

$4x-3y=24$ -----> equation B

Solve the system of equations A and B by substitution

substitute equation A in equation B

$4x-3(2x-18)=24$

solve for x

$4x-6x+54=24\\2x=30\\x=15\ m$

Find the value of y

$y=2(15)-18=12\ m$

therefore

The dimensions of rectangle are

Length: 15 meters

Breadth: 12 meters