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John has a large piece of artwork on an 8 foot by 6 foot canvas. Roberta has a piece of artwork on a canvas that is 25% smaller than John's. If the e of length to width is the same for the two canvases, what are the dimensions of Roberta's canvas?

a) 2 feet by 1.5 feet
b) 4 feet by 3 feet
c) 6 feet by 4.5 feet
d) 10 feet by 7.5 feet

User Flowerking
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1 Answer

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Final answer:

To determine Roberta's canvas size, 25% is subtracted from John's 8x6 feet canvas area, ensuring the same scale factor, resulting in a canvas size of 6 feet by 4.5 feet.

Step-by-step explanation:

John has a large piece of artwork on an 8 foot by 6 foot canvas. Roberta has a piece of artwork on a canvas that is 25% smaller than John's. To find the dimensions of Roberta's canvas, we need to calculate 25% of John's canvas dimensions and subtract that from the original size, ensuring that the scale factor of length to width remains the same.

First, find the area of John's canvas: 8 feet × 6 feet = 48 square feet.

Calculate 25% of the area of John's canvas: 25% of 48 square feet = 0.25 × 48 = 12 square feet.

Deduct the reduced area from John's canvas area to find Roberta's canvas area: 48 square feet - 12 square feet = 36 square feet.

To maintain the same scale factor, the dimensions of Roberta's canvas must also have a ratio of 4:3 (8:6 simplified). We need to find two numbers that multiply to 36 and have this ratio. These numbers are 6 feet and 4.5 feet, so Roberta's canvas dimensions are 6 feet by 4.5 feet.

Therefore, the correct answer is c) 6 feet by 4.5 feet.

User Tenika
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