Rectangle length The lenghts of arectangle is two inches mor

Rectangle length

The lenghts of arectangle is two inches more than its width.

If the lenghth is increased by four inches and the width is doubled, a new rectangle is formed whose area is 75 square units more than the old area. What are the dimensions of the original rectangle ?

Solution

We\'ll establish the dimensions of the original rectangle:

- the width: x

- the length: x + 2

The area of the original rectangle is:

A1 = x*(x+2)

We\'ll establish the dimensions of the new formed rectangle:

- the width: 2x

- the length: (x + 2) + 4 = x + 6

The area of the new rectangle is:

A2 = 2x(x+6)

We know from enunciation that the new area is 75 more than the area of the original rectangle.

A2 = 75 + A1

2x(x+6) = 75 + x(x+2)

We\'ll remove the brackets:

2x^2 + 12x = 75 + x^2 + 2x

We\'ll move all terms to one side:

2x^2 + 12x - 75 - x^2 - 2x = 0

We\'ll combine like terms:

x^2 + 10x - 75 = 0

We\'ll apply the quadratic formula:

x1 = [-10+sqrt(100 + 300 )]/2

x1 = (-10+20)/2

x1 = 5

x2 = (-10-20)/2

x2 = -15

Since the measure of a side cannot be negative, we\'ll reject the second negative value.

So, the width of the original rectangle is:

x = 5 inches

the length: x + 2 = 7 inches