The length of a rectangle exceeds its breadth by 9 cm. If length and b

1.	The length of a rectangle exceeds its breadth by 9 cm. If length and breadth are each increased by 3 cm, the area of the new rectangle will be 84 cm2 more than that of the given rectangle. Find the length and breadth of the given rectangle.
Answer» Let the breadth of the rectangle be x meter Length of the rectangle be (x + 9) meter Area of the rectangle length×breadth = x(x +9) m² When length and breadth increased by 3cm then, New length = x + 9 + 3 = x + 12 New breadth = x + 3 So, Area is (x + 12) (x + 3) = x (x + 9) + 84 x² + 15x + 36 = x² + 9x + 84 15x – 9x = 84 – 36 6x = 48 x = 48/6 = 8 ∴ Length of the rectangle (x + 9) = (8 + 9) = 17cm and breadth of the rectangle is 8cm.

The length of a rectangle exceeds its breadth by 9 cm. If length and breadth are each increased by 3 cm, the area of the new rectangle will be 84 cm2 more than that of the given rectangle. Find the length and breadth of the given rectangle.

Answer»

Let the breadth of the rectangle be x meter

Length of the rectangle be (x + 9) meter

Area of the rectangle length×breadth = x(x +9) m²

When length and breadth increased by 3cm then,

New length = x + 9 + 3 = x + 12

New breadth = x + 3

So, Area is

(x + 12) (x + 3) = x (x + 9) + 84

x² + 15x + 36 = x² + 9x + 84

15x – 9x = 84 – 36

6x = 48

x = 48/6

= 8

∴ Length of the rectangle (x + 9) = (8 + 9) = 17cm and breadth of the rectangle is 8cm.