Question

The length of a rectangle exceeds its length and breadth by 3cm.If each of the length and breadth are increased by 2cm, the area of the new rectangle will be 58cm( square) more than Of the original rectangle.Find the length and breadth of the original rectangle.

Answer 1

Answer:

The length of the rectangle is 15cm and the breadth is 12cm.

Step-by-step explanation:

1. The length exceeds the breadth by 3cm so let the breadth of the rectangle be x and the length be x+3
2. Area of the original rectangle = length × breadth = x(x+3) = x²+3x
3. Length and breadth increased by 2cm. Therefore the length is now x+2 and the breadth is x+3+2 which is x+5
4. Since the area of the new rectangle is 58cm² more than the original rectangle, the equation can be written as: (x+2)(x+5)=x²+3x+58
5. By solving it, x²+5x+2x+10=x²+3x+58
6. x² can get cancelled from both sides as they have the same sign(positive). So, 7x+10=3x+58
7. By transposition, 7x-3x=58-10
8. 4x=48
9. x=48 ÷ 4
10. x=12
11. Therefore breadth = x = 12cm and length = x+3 = 12+3 = 15cm

Hope you've got your doubt clarified!