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The area of a rectangular floor is 56 square feet. If both the length and the width of the rectangular floor are integers, the l
The area of a rectangular floor is 56 square feet. If both the length and the width of the rectangular floor are integers, the l
admin
2021-10-21
69
问题
The area of a rectangular floor is 56 square feet. If both the length and the width of the rectangular floor are integers, the length can have how many possible values?
选项
A、4
B、6
C、10
D、8
E、7
答案
A
解析
设长方形的长和宽分别是a和b,那么ab=56,现在求长边的值有多少个可能的值。显然由于长和宽都是整数,那么必然都是56的因子,而由于是长方形,那么a>b,不等式两边都乘以口,得到a
2
>ab=56,那么a>
,所以题目变成求56有多少个大于
的因子,56=2
3
×7,共有(3+1)×(1+1)=8个因子,那么大于
的因子为8/2=4,因此长方形的长有4种可能值。
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