Question

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 the scale - factor formula

The formula for scale - factor $k$ is $k=\frac{\text{dimensions of scaled copy}}{\text{dimensions of original}}$. Given $k = 2$.

Step2: Calculate the base of the original parallelogram

If the base of the scaled - copy is $b_{s}=10$ cm and $k = 2$, then using the formula $k=\frac{b_{s}}{b_{o}}$, we can solve for the base of the original parallelogram $b_{o}$. Rearranging gives $b_{o}=\frac{b_{s}}{k}$. Substituting $b_{s}=10$ cm and $k = 2$, we get $b_{o}=\frac{10}{2}=5$ cm.

Step3: Calculate the height of the original parallelogram

If the height of the scaled - copy is $h_{s}=6$ cm and $k = 2$, then using the formula $k=\frac{h_{s}}{h_{o}}$, we can solve for the height of the original parallelogram $h_{o}$. Rearranging gives $h_{o}=\frac{h_{s}}{k}$. Substituting $h_{s}=6$ cm and $k = 2$, we get $h_{o}=\frac{6}{2}=3$ cm.

Answer:

Base: 5 cm, Height: 3 cm