(v) The area of a rectangle gets reduced by 9 square units, if its len

1.	(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by5 units and breadth is increased by 3 units. If we increase the length by 3 units andthe breadth by 2 units, the area increases by 67 square units. Find the dimensionsof the rectangle.Plz answer, Dont spam!!
Answer» 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.

(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by5 units and breadth is increased by 3 units. If we increase the length by 3 units andthe breadth by 2 units, the area increases by 67 square units. Find the dimensionsof the rectangle.Plz answer, Dont spam!!

Answer»

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

−183+12

−y

9+10

⇒x=

323

=17 and y=

171

=19

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