1985 AMC 8 Problem 19

Attempt Problem 19 of the 1985 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1985 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

19.

If the length and width of a rectangle are each increased by 10%,10\%, then the perimeter of the rectangle is increased by
1%1\%
10%10\%
20%20\%
21%21\%
40%40\%
Answer: B
Concepts:percentageperimeter
Small hint:
The perimeter is 2(ℓ+w)2(\ell + w)
Big hint:
Multiplying both ℓ\ell and ww by 1.11.1 multiplies the whole perimeter by 1.11.1
Solution:
The new perimeter is 2(1.1ℓ+1.1w)=1.1⋅2(ℓ+w),2(1.1\ell + 1.1w) = 1.1 \cdot 2(\ell + w), which is 1.11.1 times the old perimeter.
That is a 10%10\% increase.
Thus, the correct answer is B .
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