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What is the length of a diagonal of a rectangle that has width 5 and perimeter 34 ?

admin2014-08-13  10
问题 What is the length of a diagonal of a rectangle that has width 5 and perimeter 34 ?
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答案13
解析 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.

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,
52+ 122 = D2
25+ 144 = D2
169 = D2
13 = D
The length of the diagonal is 13, so the correct answer is 13.
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