Question

this parallelogram is a scaled copy. it was scaled by a factor of 1/2. 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 2

Explanation:

Step1: Recall scaling - factor formula

If the scaled - copy is scaled by a factor of $k$ from the original, and we know the dimensions of the scaled - copy, to find the original dimensions, we use the formula $x_{original}=\frac{x_{scaled}}{k}$. Here, $k = \frac{1}{2}$, so to go back to the original, we multiply the dimensions of the scaled - copy by $\frac{1}{k}=2$.

Step2: Calculate the original base

The base of the scaled - copy is $10$ cm. The original base $b_{original}=10\times2 = 20$ cm.

Step3: Calculate the original height

The height of the scaled - copy is $6$ cm. The original height $h_{original}=6\times2 = 12$ cm.

Answer:

Base: 20 cm
Height: 12 cm