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Ryan, Engineer

Category: Math

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Experience: B.S. in Civil Engineering

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A rectangle has an area of 10^2. If each side has its length

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A rectangle has an area of 10^2. If each side has its length tripled, what is the new area?Please explain what calculations are necessary to get the correct answer.

Hi, Thank you for using the site. I'll be happy to help you with this. Since each side triples in length, the area will be multiplied by a factor of 3 * 3 = 9. So an area of 10^2 (which is equal to 100) will become an area of 9 * 100 = 900 square units. To see that this works, imagine that this rectangle has a length of 10 units and a width of 10 units. (Of course, that makes this a square, but a square is still a rectangle.) If the length and width are both tripled, then they are each 30 units instead of 10 units. The new area would be 30 * 30 = 900 square units, which matches what we got before. You can also see this in symbolic form. The area of the original rectangle is L * W. When each of them triple, the new area is 3L * 3W = 3 * 3 * L * W = 9 * L * W, which is again 9 times the original area. Please feel free to ask if you have any additional questions about this. Thanks, Ryan

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