Dimensions of a rectangle
Which are the dimensions of the original rectangle if it's length is 2 times the width and if the length is decreased by 5 units and the width is increased by 5 units, the area is increased by 75 square units?
Let's establish the dimensions of the original rectangle:
x=width of the rectangle, in umits;
2x=length of the rectangle, in units.
We'll put into equation the enunciation: The area of the first rectangle + 75 is equal to the area of the second rectangle.
2x*x + 75 = (2x-5)(x+5)
So the dimensions of the original rectangle are: the width x=20 units and the length is 2x=40units.
Let the breadth and length of the rectangle be x and 2x.
The its area = 2x^2.
After increasing the breadth by 5 and decreasing the length by 5 unita the are = (x+5)(2x-5).
Given that the area (x+5)(2x-5) = 2x^2+75. Or
2x^2+5x-25 = 2x^2+75. Or
5x = 75+25 = 100. Or
x = 100/5 =20 is the width and the length = 2x =2*20 = 45.