Question

this rectangle is a scaled copy. it was scaled by a scale factor of 1/2. suppose you want to scale it back to its original size. what is the length and width of the original rectangle? 3 in 10 in original rectangle scaled copy length in 10 in width in 3 in

Explanation:

Step1: Recall scale - factor formula

If the scale - factor $k=\frac{1}{2}$, and the length and width of the scaled - copy are $l_{s}$ and $w_{s}$, and the length and width of the original rectangle are $l_{o}$ and $w_{o}$, then $l_{s}=k\times l_{o}$ and $w_{s}=k\times w_{o}$. To find the original dimensions, we use the formula $l_{o}=\frac{l_{s}}{k}$ and $w_{o}=\frac{w_{s}}{k}$.

Step2: Calculate the original length

Given $l_{s} = 10$ in and $k=\frac{1}{2}$, then $l_{o}=\frac{10}{\frac{1}{2}}=10\times2 = 20$ in.

Step3: Calculate the original width

Given $w_{s}=3$ in and $k = \frac{1}{2}$, then $w_{o}=\frac{3}{\frac{1}{2}}=3\times2=6$ in.

Answer:

Length: 20 in
Width: 6 in