Final answer:
The original width of the rectangle is 4 cm and the original length is 8 cm.
Step-by-step explanation:
To find the original dimensions of the rectangle, we'll set up an equation based on the given information.
Let's assume the original width of the rectangle is x cm.
According to the problem, the original length of the rectangle is twice its width, so it would be 2x cm.
The area of a rectangle is found by multiplying its length and width: Area = Length x Width.
Since both the length and width are decreased by 4 cm, the new dimensions would be (2x-4) cm and (x-4) cm respectively.
According to the problem, the new area is decreased by 164 cm², so we can set up the equation:
Area = (2x-4) cm * (x-4) cm
= (2x cm - 4 cm) * (x cm - 4 cm)
= 2x² cm² - 4x cm - 8x cm + 16 cm²
= 2x² cm² - 12x cm + 16 cm²
Now we can equate this to the original area:
2x² cm² - 12x cm + 16 cm²
= 2x² cm²
By canceling out the common terms on both sides and rearranging the equation, we get:
-12x cm + 16 cm² = 0
Solving this equation, we find that x = 4 cm. Therefore, the original width of the rectangle is 4 cm and the original length is 8 cm.