Question

this parallelogram is a scaled copy. it was scaled by a factor of 2. suppose you want to scale it back to its original size. what are the base and height of the original parallelogram? to scale back to the original, use a scale factor of 1/2.

Explanation:

Step1: Recall the scale - factor relationship

If the scale - factor from the original to the scaled copy is $k$, then to go from the scaled copy back to the original, the scale - factor is $\frac{1}{k}$. Here $k = 2$, so the scale - factor to go back to the original is $\frac{1}{2}$.

Step2: Calculate the base of the original parallelogram

The base of the scaled - copy is $8$ cm. Using the scale - factor $\frac{1}{2}$, the base of the original parallelogram $b=\frac{8}{2}=4$ cm.

Step3: Calculate the height of the original parallelogram

The height of the scaled - copy is $2$ cm. Using the scale - factor $\frac{1}{2}$, the height of the original parallelogram $h = \frac{2}{2}=1$ cm.

Answer:

Base: $4$ cm, Height: $1$ cm