Question

3. Solve the following problems :
(i) If the length of a rectangle is increased by
2 cm and breadth is reduced by 2 cm, the area
is reduced by 28 cm2. If the length is reduced
by 1 cm and breadth is increased by 2 cm, the
area increased by 33 cm. Find the length and
breadth of the rectangle.
Solution : (i) Use variables x and y for the length
and breadth respectively. (ii) Form two
simultaneous equations from the given conditions
and solve.​

Answer 1

Answer:

let length be x

breadth=y

area =xy

In first case, the the length is increased by 2 and breadth is reduced by 2

New length=x+2

New breadth=y-2

New area=(x+2)(y-2)

xy-2x+2y-4

according to question,the area decreases by 28cm

xy-2x+2y-4=xy-28

2y-2x=-28+4

2(y-x)=-24

y-x=-12...(1)

In another case,length=x-1

breadth=y+2

Area = (x-1)(y+2)

=xy+2x-y-2

Now the area increases by 33

so,xy+2x-y-2=xy+33

2x-y=35...(2)

Now on adding (1) and (2) we have,

y-x+2x-y=-12+35

x=23cm

putting the value of x in (1) we get

y-23=-12

y=-12+23

y=11

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Answer 2

Step-by-step explanation:

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