Question

Q.4.The area of a rectangle (of length x units and breadth y units) is xy sq. units.If the length is increased by 5 units and breadth is deccreased by 3 units, then the new area is (a) (xy+5) sq. units (b)(xy-15) sq. units (c)(x-5)(y-3) sq. units (d)(x+5)(y-3) sq. units challenge give the correct answer​

Answer 1

Step-by-step explanation:

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

​

=9

Hence, the length and breadth of the rectangle are 17 units and 9 units respectively.