Question

The length of a rectangle is trice its breadth.if its length is decreased by 9 cm and breadth is increased by 9 cm , the area of the rectangle is increased by 81 sq. cm. find the length of the rectangle.

Answer 1

Answer:

Let breadth of rectangle = x

Length of rectangle = 3x

Area of rectangle = 3x × x = 3x^2

According to question,

Length of rectangle = (3x - 9) cm

Breadth of rectangle = (x + 9) cm

Area of rectangle = (3x^2 + 81) sq. cm

Area = length × breadth

(3x^2 + 81) = (3x - 9) (x + 9)

(3x^2 + 81) = 3x^2 + 27x - 9x - 81

3x^2 + 81 = 3x^2 + 18x - 81

81 + 81 = 18x

162 = 18x

x = 162/18

x = 9

So, Length of rectangle = ( 3 × 9 -9 )

= 18 cm