Question

the length of a rectangular field is increased by 3 and breadth decreased by 3 then the area decreased by 18 m square. but if length and breadth both are increased by 3m. its area is increased by 60 m square. find the length and breadth of the field​

Answer 1

Let the length of the rectangle be x metres and the breadth be y metres.

Area of the rectangle=length×breadth

=x×y=xy sq. metres

From the given information, we have,

(x+3)×(y−4)=xy−67

and(x−1)×(y+4)=xy+89

(x+3)×(y−4)=xy−67

=>xy−4x+3y−12=xy−67

=>4x−3y=55

=>4x=3y+55....(i)

Also,(x−1)×(y+4)=xy+89

=>xy+4x−y−4=xy+89

=>4x−y=93....(ii)

Substituting equation (i) in equation (ii), we get,

4x−y=93

=>3y+55−y=93

=>2y=38

=>y=19

Substituting y=19 in equation (i), we get,

4x=3y+55

=>4x=3(19)+55

=>4x=112

=>x=28

Therefore, length of rectangle =x=28 metres

breadth of rectangle =y=19 metres

Answer 2

Answer:

Let’s assume the length and breadth of the rectangle be x units and y units respectively. Hence, the area of rectangle = xy sq.units From the question we have the following cases, According to the question, Case 1: Length is increased by 3 metres ⇒ now, the new length is x+3 Breadth is reduced by 4 metres ⇒ now, the new breadth is y-4 And it’s given, the area of the rectangle is reduced by 67 m2 = xy – 67. So, the equation becomes xy – 67 = (x + 3)(y – 4) xy – 67 = xy + 3y – 4x – 12 4xy – 3y – 67 + 12 = 0 4x – 3y – 55 = 0 —— (i) Case 2: Length is reduced by 1 m ⇒ now, the new length is x-1 Breadth is increased by 4 metre ⇒ now, the new breadth is y+4 And it’s given, the area of the rectangle is increased by 89 m2 = xy + 89. Then, the equation becomes xy + 89 = (x -1)(y + 4) 4x – y – 93 = 0 —— (ii) Solving (i) and (ii), Using cross multiplication, we get x = 224/8 x = 28 And, y = 152/8 y = 19 Therefore, the length of rectangle is 28 m and the breadth of rectangle is 19 m.

Step-by-step explanation:

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