Question

look at this rectangle. 6 units 3 units which could be the dimensions of a scaled copy of the rectangle? 4 units by 2 units 9 units by 6 units 12 units by 9 units 5 units by 2 units what scale factor was used to make the scaled copy? 1/2 3/4 2/3 2

Explanation:

Step1: Calculate the ratio of original rectangle

The original rectangle has dimensions \(6\) units (length) and \(3\) units (width). The ratio of length to width is \(\frac{6}{3}=2\).

Step2: Check the ratio of each option

• For \(4\) units by \(2\) units: \(\frac{4}{2} = 2\).
• For \(9\) units by \(6\) units: \(\frac{9}{6}=\frac{3}{2}

eq2\).

• For \(12\) units by \(9\) units: \(\frac{12}{9}=\frac{4}{3}

eq2\).

• For \(5\) units by \(2\) units: \(\frac{5}{2}

eq2\).

Step3: Calculate the scale factor

If the original length \(l = 6\) and the new length \(l_{new}=4\), let the scale factor be \(k\). We know that \(l_{new}=k\times l\). So \(k=\frac{l_{new}}{l}=\frac{4}{6}=\frac{2}{3}\) (checking with width: original width \(w = 3\), new width \(w_{new}=2\), \(k=\frac{w_{new}}{w}=\frac{2}{3}\))

Answer:

First part: \(4\) units by \(2\) units.
Second part: \(\frac{2}{3}\)