Tran planned a rectangular pool and made a scale drawing using centimeters as the unit of measurement. He originally planned for the length of the pool to be 40 m but decided to change it to 32 m. If the length of the pool in his scale drawing is 8 cm, which statement about the change of scale is true?

One cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale.

One cm represented 40 m in the first scale, but now 1 cm represents 32 m in the second scale.

One cm represented 1 m in the first scale, but now 1 cm represents 5 ft in the second scale.

One cm represented 4 m in the first scale, but now 1 cm represents 5 m in the second scale.

Question

Mathematics

Iyana Short

16 August, 20:22

Tran planned a rectangular pool and made a scale drawing using centimeters as the unit of measurement. He originally planned for the length of the pool to be 40 m but decided to change it to 32 m. If the length of the pool in his scale drawing is 8 cm, which statement about the change of scale is true?

One cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale.

One cm represented 40 m in the first scale, but now 1 cm represents 32 m in the second scale.

One cm represented 1 m in the first scale, but now 1 cm represents 5 ft in the second scale.

One cm represented 4 m in the first scale, but now 1 cm represents 5 m in the second scale.

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Answers (1)

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Saunders · Answer 1

One cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale. First of all, determine the old and new scale measurements. Old drawing has the pool 40 m long and the scale drawing is 8 cm. So 40 m / 8 cm = 5 m/cm scale. (5 meters represented for each cm) The new plan has the pool being 32 m long and the drawing still is showing 8 cm. So 32 m / 8 cm = 4 m/cm scale (4 meters represented for each cm) Now look at the available choices and see which describes the situation. One cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale. - This one matches what we calculated. So this is the correct choice. One cm represented 40 m in the first scale, but now 1 cm represents 32 m in the second scale. - This is way off. With that scale, the pool in the old design would be 8 * 40 = 320 meters long and the new design would be 256 meters long. Both several times longer than a football field. That's not a pool, that's a small lake. One cm represented 1 m in the first scale, but now 1 cm represents 5 ft in the second scale. - Wrong again. Where in the original question were any measurements made in feet? One cm represented 4 m in the first scale, but now 1 cm represents 5 m in the second scale. - Also wrong, but slightly tricky. Just remember, the original plan was to have a pool of 40 meters length and the new plan was to have a pool of 32 meters length. Since the new plan is the smaller pool, the new scale is the smaller scale.