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25 Jul 2024, 00:39
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Difficulty:
(N/A)
Question Stats:
50% (00:55) correct
50% (00:19) wrong based on 4 sessions
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What is the length of a diagonal of a rectangle that has width 5 and perimeter 34?
03 Aug 2024, 05:17
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Official Explanation
In this question, you are given that a rectangle has width 5 and perimeter 34, and you are asked to find the length of a diagonal of the rectangle. Let L and W represent the length and width of the rectangle, respectively, and let D represent the length of a diagonal. Note that you are not given L but you are given that W = 5 and that the perimeter is 34. Because the perimeter is equal to L + L + W + W, or 2(L + W), you can determine L as follows.
From the figure, you can see that the diagonal is the hypotenuse of a right
triangle with legs of length 5 and 12. Therefore, by the Pythagorean theorem,
In this question, you are given that a rectangle has width 5 and perimeter 34, and you are asked to find the length of a diagonal of the rectangle. Let L and W represent the length and width of the rectangle, respectively, and let D represent the length of a diagonal. Note that you are not given L but you are given that W = 5 and that the perimeter is 34. Because the perimeter is equal to L + L + W + W, or 2(L + W), you can determine L as follows.
2(L + 5) = 34
L + 5 = 17
L = 12
The following figure shows a rectangle of length 12, width 5, and diagonal of length D.L + 5 = 17
L = 12
From the figure, you can see that the diagonal is the hypotenuse of a right
triangle with legs of length 5 and 12. Therefore, by the Pythagorean theorem,
\(5^2+12^2=D^2\)
\(25+144=D^2\)
169=D
13=D
The length of the diagonal is 13, so the correct answer is 13.\(25+144=D^2\)
169=D
13=D
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