Question

If in a rectangle, the length is increased and
breadth reduced each by 2 metres, the area
is reduced by 28 sq. metres. If the length is
reduced by 1 metre and breadth increased
by 2 metres, the area increases by 33 sq.
metres. Find the length and breadth of the
rectangle.​

Answer 1

Answer:

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Step-by-step explanation:

Let x = length & breadth = y

Area = x.y=A

(i) (x+2)(y−2)=(A−26)⇒xy−2x+2y−4=xy−28⇒y−x=−12 ...(1)

(ii) (x−1)(y+2)=A+33⇒xy+2x−y−2=xy+33⇒2x−y=35 ...(2)

adding both equation

x=23,y−x+2x−y=−12+35⇒x=23

Placing in equation (1)

y−23=−12⇒y=11

Answer 2

Step-by-step explanation:

let the length be l and breadth be b

Now,

Area of rectangle = lb

According to the question,

area of rectangle is reduced by 28 square metres when length is increased and breadth is reduced each by 2 metres

then,(l+2)(b-2) = lb-28

lb–2l+2b–4 = lb–28

–2l+2b = -28+4

–2l+2b = -24………………….(1)

and,

area of rectangle is increased by 33 square metres when length is reduced by one and breadth is increased by 2 metres

then,(l-1)(b+2) = lb+33

lb+2l-b-2 = lb+33

2l-b = 33+2

2l-b =35…….…...............………(2)

adding eq(1) and (2)

2b–b = -24+35

b = 11

put b= 11 in eq(2),we get

2l = 35+b

2l = 35+11

2l = 46

l = 23metres

hence the length of the rectangle is 23 metres and the breadth of the rectangle is 11 metres.