Question

The length of a room exceeds its breadth by 3 metre if the length is increased by 3 metre and the breadth is decreased by 2 the area remains the same find the length of the room

Answer 1

Answer:

Length of the room is 15 metre

Step-by-step explanation:

Let the breadth of room be $x$ metre

Thus, the length of room $= x + 3$ metre

Now, Area of rectangle is calculated as

$Area = Length \times Breadth\\\\ Area = x(\,x + 3)\,$

Now, New length of room $= (\,x + 3)\, + 3 = x + 6$ metre

New breadth of room $= x - 2$ metre

Given that area of room remains the same.

Thus, we have

$Area = (\,x + 6)\,(\,x - 2)\,\\\\ x(\,x + 3)\, = (\,x + 6)\,(\,x - 2)\,\\\\ x^2 + 3x = x^2 + 6x - 2x - 12\\\\ 3x = 4x - 12\\\\ 4x - 3x = 12\\\\x = 12$

Thus, breadth of  room $= 12$ metre

Length of room $= 12 + 3 = 15$ metre