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basil was shown this enlargement, and he was asked to find the perimete…

Question

basil was shown this enlargement, and he was asked to find the perimeter of the enlarged shape. his work is shown below.
figures not drawn to scale.
basils work
scale factor
scale a
scale b
perimeter
where, if any, did basil first make a mistake in his work?
hint: check to make sure each of the 4 steps is valid.
o basil made a mistake finding the scale factor.
o basil made a mistake when finding the length of either side a or side b.
o basil made a mistake finding the perimeter.
o basil did not make any mistakes in his work.

Explanation:

Brief Explanations
  1. First, analyze the scale factor: The original side (let's assume the small figure has a side of length 6, and the enlarged one has 24? Wait, no, looking at the small figure: the bottom side (maybe side B) is 6, and the enlarged one's side B? Wait, the small figure: let's check the sides. The small figure has a bottom side (maybe side B) of 6, and the enlarged one's side B? Wait, Basil's scale factor: he took 24/6 = 4. But wait, the small figure's side A (the slant side) is 2, so enlarged side A should be 24=8 (which he did). Then side B: small side B is 6? Wait no, maybe the small figure's bottom is 6, and the vertical sides? Wait, no, let's check the perimeter. The small figure: let's count the sides. The small figure: top is a pentagon? Wait, the small figure has sides: 2 (left), 2 (right), 6 (bottom), 1 (top left), 1 (top right)? Wait, no, the small figure: maybe the sides are 2, 2, 6, and two sides of 1? Wait, no, the small figure's perimeter: 2 + 2 + 6 + 1 + 1 = 12? Wait, Basil's perimeter calculation: 24 + 16 + 8 + 8 = 56? Wait, no, let's check his steps. Wait, the mistake: when calculating the perimeter, he should scale all sides by the scale factor. Wait, no, first, check the side lengths. Wait, the small figure: let's say the bottom side (side B) is 6, and the enlarged side B is 24? Wait, no, 64=24, that's correct. The slant side (side A) is 2, so 24=8, correct. Then the other sides: the small figure has vertical sides of 2? Wait, no, the small figure: left side is 2, right side is 2, top has two sides of 1, bottom is 6. So perimeter of small figure: 2 + 2 + 6 + 1 + 1 = 12. Enlarge by scale factor 4: perimeter should be 124=48. But Basil calculated 24 + 16 + 8 + 8 = 56. Wait, but let's check his side B: he said side B is 44=16? Wait, no, original side B (small) is 6, so 64=24, but he wrote 44=16? Wait, no, maybe I misread. Wait, the table: Scale factor: 24/6=4 (correct). Side A: 42=8 (correct, since small side A is 2). Side B: 44=16? Wait, that's the mistake! Wait, original side B (small) is 6, so 64=24, but he did 44=16. Oh! So he made a mistake in finding the length of side B. Because side B (small) is 6, so 64=24, but he calculated 44=16. So the mistake is in finding the length of side B (or side A? No, side A was 24=8). Wait, no, the option: "Basil made a mistake when finding the length of either side A or side B." Wait, no, side B: he should have 64=24, but he did 44=16. So he messed up side B's length. So the correct option is "Basil made a mistake when finding the length of either side A or side B." Wait, no, let's re-express. Wait, the small figure's side B (bottom) is 6, so enlarged side B is 64=24. But in his work, he wrote "Side B: 4×4=16", which is wrong. So he made a mistake in side B's length. So the option is "Basil made a mistake when finding the length of either side A or side B." Wait, but side A was correct (24=8). Side B was wrong (64=24, but he did 44=16). So the mistake is in side B's length, so the option is "Basil made a mistake when finding the length of either side A or side B." Wait, but let's check the options:

Options:

  1. Basil made a mistake finding the scale factor. (No, 24/6=4 is correct)
  1. Basil made a mistake when finding the length of either side A or side B. (Yes, because side B: he should have 64=24, but he did 44=16)
  1. Basil made a mistake finding the perimeter. (After correcting side B, perimeter would be 24 + 8 + 8 + 24? No, wait, no, let's re-express. Wait, maybe the small figure's side B is 4, not 6? Wait, maybe I misread the small figure. The small fig…

Answer:

Basil made a mistake when finding the length of either side A or side B. (The option corresponding to this statement, e.g., if the options are labeled as:

A. Basil made a mistake finding the scale factor.

B. Basil made a mistake when finding the length of either side A or side B.

C. Basil made a mistake finding the perimeter.

D. Basil did not make any mistake in his work.

Then the answer is B. Basil made a mistake when finding the length of either side A or side B.)