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