Question

figures not drawn to scale.
jordanas work
scale factor \t $\frac{4}{12} = \frac{1}{3}$
slide a \t $30 \times \frac{1}{3} = 10$
slide b \t $30 \times \frac{1}{3} = 10$
perimeter \t $10 + 10 + 4 + 4 = 28$
where, if any, did jordana first make a mistake in her work?
○ jordana made a mistake when finding the scale factor.
○ jordana made a mistake when she calculated the length of slide a.
○ jordana made a mistake when she calculated the length of slide b.
○ jordana did not make any mistakes in her work.
mark this and return

Explanation:

To determine the scale factor, we assume the original length corresponding to the new length of 4 (for the sides of length 4 in the scaled figure) is 12 (since \(\frac{4}{12}=\frac{1}{3}\) is the scale factor, meaning the scaled figure is \(\frac{1}{3}\) the size of the original). For side A, if the original length is 30, then the scaled length is \(30\times\frac{1}{3} = 10\), which is correct. However, for side B, we need to check if it should also be scaled from the same original length or a different one. If the original figure has two sides of length 30 (for side A and side B) and two sides of length 12 (for the other two sides), then when scaling, the two sides corresponding to the original 12 would scale to 4 (since \(12\times\frac{1}{3}=4\)), and the two sides corresponding to the original 30 would scale to 10 (as done for side A). But if side B is supposed to be scaled from a different original length (or if there's a mis - assumption about which sides correspond), Jordana incorrectly assumed side B has the same original length as side A for scaling. In a rectangle (assuming the figure is a rectangle with length 30 and width 12), the perimeter of the original rectangle is \(2\times(30 + 12)=84\), and the perimeter of the scaled rectangle (scale factor \(\frac{1}{3}\)) should be \(84\times\frac{1}{3}=28\), but the mistake is in the calculation of side B. Wait, no, actually, if the original figure has length 30 and width 12, then the scaled length (side A) is \(30\times\frac{1}{3}=10\) and the scaled width (side B) should be \(12\times\frac{1}{3} = 4\), not \(30\times\frac{1}{3}=10\). So Jordana made a mistake when calculating the length of side B, she should have used the original width (12) to scale, not the original length (30).

Answer:

Jordana made a mistake when she calculated the length of side B.