Question

(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by
5 units and breadth is increased by 3 units. If we increase the length by 3 units and
the breadth by 2 units, the area increases by 67 square units. Find the dimensions
of the rectangle.

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Answer 1

Step-by-step explanation:

ANSWER

Let the length and breadth of the rectangle be x and y units respectively. Then,

Area =xy sq. units.

If length is reduced by 5 units and the breadth is increases by 3 units, then area is reduced by 9 square units.

∴xy−9=(x−5)(y+3)

⇒xy−9=xy+3x−5y−15

⇒3x−5y−6=0 ...(i)

When length is increased by 3 units and breadth by 2 units, the area is increased by 67 sq. units.

∴xy+67=(x+3)(y+2)

⇒xy+67=xy+2x+3y+6

⇒2x+3y−61=0 ...(ii)

Thus, we get the following system of linear equations:

3x−5y−6=0

2x+3y−61=0

By using cross-multiplication, we have

305+18

x

=

−183+12

−y

=

9+10

1

⇒x=

19

323

=17 and y=

19

171

=19

Hence, the length and breadth of the rectangle are 17 units and 19 units respectively.