Question

b) 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 answer is in attachment.......

Answer 2

Answer:

Length = 15 m

Breadth = 12 m

Step-by-step explanation:

Consider:

Let the length = x meters

Let the breadth = y meters

The area of the rectangle = xy m²

A/q,

In case 1,

(x+1)(y-2)=xy-20

⇒xy-2x+y-2=xy-20

⇒ -2x+y+18=0

⇒2x-y-18=0-----------------------(i)

In case 2,

(x-3)(y+4)=xy+12

⇒xy+4x-3y-12=xy+12

⇒4x-3y-24=0--------------------(ii)

Multiply 2 to (i):

2(2x-y-18=0)

⇒4x-2y-36=0--------------------(iii)

Now subtract (ii) from (iii):

  4x-2y-36=0

-

  4x-3y-24=0

(-)   (+) (+)

-----------------------

y-12=0

⇒y=12 meters

Now,

$x=\frac{24+3y}{4}$             [from (ii)]

⇒x=36+24/4

⇒x=60/4

⇒x=15 meters

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