Question

POP

(ii) The area of a rectangle reduces by 20 m2, if its length is increased by Im and the
breadth is reduced by 2 m. The area increases by 12 m², if the length is reduced
by 3 m and the breadth is increased by 4 m. Find the dimensions of the rectangle.

Answer 1

The dimensions of rectangle are

Length: 15 meters

Breadth: 12 meters

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