Question

In a rectangle, if the length is increased by 3 metres and breadth is decreased by 4 metres, the area of the triangle is reduced by 67 square metres. If length is reduced by 1 metre and breadth is increased by 4 metres, the area is increased by 89 sq. metres. Find the dimension of the rectangle.

Answer 1

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.