The length of a rectangle is 8 feet more than its width. If the width is increased by 4 feet and the length is decreased by 5 feet, the area will remain the same. Find the dimensions of the original rectangle.
w(w+8) = (w+4)(w+8 - 5)
find w, and then w+8
To solve this problem, let's start by assigning variables to the dimensions of the rectangle. Let's say the width of the rectangle is 'w' feet and the length is 'l' feet.
According to the problem, the length of the rectangle is 8 feet more than its width. So, we can write the equation:
l = w + 8
Next, we are given that if the width is increased by 4 feet (w + 4) and the length is decreased by 5 feet (l - 5), the area will remain the same.
The area of a rectangle is given by the formula: Area = length * width.
So, the original area is A = l * w and the new area is A' = (l - 5) * (w + 4).
Since we are told that the areas are equal, we can set up the equation:
A = A'
l * w = (l - 5) * (w + 4)
Now we can substitute the value of 'l' from the first equation into the second equation:
(w + 8) * w = ((w + 8) - 5) * (w + 4)
Simplifying this equation:
w^2 + 8w = (w + 3)(w + 4)
Expanding the right side of the equation:
w^2 + 8w = w^2 + 7w + 12
Now we can cancel out the common terms on both sides of the equation:
8w = 7w + 12
Subtracting 7w from both sides gives:
w = 12
Therefore, the width of the original rectangle is 12 feet.
Using the first equation, we can find the length:
l = w + 8 = 12 + 8 = 20
So, the dimensions of the original rectangle are:
Width = 12 feet
Length = 20 feet