This is the basic and conceptual question from linear equations in two variables in which we have been asked to find the length and breadth of a rectangle if its length decreases by 5 m and breadth increases by 3 m, its area reduces by 8 m², similarly if its we increase the length by 3m and breadth by 2m, the area is increased by 74 m².

Kindly solve the above problem

RS Aggarwal, Class 10, chapter 3E, question no 39

## Let the length of a rectangle =xm and the breadth of a rectangle =ym Then,

Area of rectangle =xym2

Condition I :Area is reduced by 8m2, when length =(x−5)m and breadth =(y+3)m

Then, area of rectangle =(x−5)×(y+3)m2

According to the question, xy−(x−5)×(y+3)=8

⇒xy−(xy+3x−5y−15)=8

⇒xy−xy−3x+5y+15=8

⇒−3x+5y=8−15

⇒3x−5y=7

Condition II:Area is increased by 74m2, when length =(x+3)m and breadth =(y+2)m

Then, area of rectangle =(x+3)×(y+2)m2

According to the question, (x+3)×(y+2)−xy=74

⇒(xy+3y+2x+6)−xy=74

⇒xy+2x+3y+6−xy=74

⇒2x+3y=74−6

⇒2x+3y=68…( ii )

On multiplying Eq.(i) by 2 and Eq.(ii) by 3, we get

6x−10y=14…( iii )

6x+9y=204…(iv)

On subtracting Eq.(i) from Eq. (ii), we get

6x+9y−6x+10y=204−14

⇒19y=190

⇒y=10

On putting the value of y=10 in Eq. (i), we get 3x−5(10)=7

⇒3x−50=7

⇒3x=57

⇒x=19

Hence, the length of the rectangle is 19m and the breadth of a rectangle is 10m