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.
Width = W.
Length = W+8.
A1 = A2.
W(W+8) = (W+4)(W+3)
W^2+8W = W^2+3W+4W+12
W = 12 Ft.
Width = W = 12 Ft.
Length = W+8 = 12+8 = 20 Ft.
To solve this problem, let's start by assigning variables.
Let's say the width of the original rectangle is "w" feet.
According to the problem, the length is then "w + 8" feet.
The area of a rectangle is given by the formula: length × width.
In this case, the area of the original rectangle is (w + 8) × w.
Now, let's consider the dimensions after the width is increased by 4 feet and the length is decreased by 5 feet.
The new width would be "w + 4" feet,
and the new length would be "w + 8 - 5" = "w + 3" feet.
Since the area remains the same, we can set up and solve an equation:
(w + 4) × (w + 3) = (w + 8) × w
Expanding this equation gives us:
w^2 + 7w + 12 = w^2 + 8w
By simplifying and collecting like terms, we can find the value of "w":
w^2 - w^2 + 7w - 8w = -12
Simplifying further:
-w = -12
Dividing both sides of the equation by -1 gives us:
w = 12
So, the width of the original rectangle is 12 feet.
And the length can be obtained using the given relation: length = width + 8.
Therefore, the length of the original rectangle is:
length = 12 + 8 = 20
Hence, the dimensions of the original rectangle are:
Width = 12 feet and Length = 20 feet.