A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. If the ratio of the brass area to the wooden area is 25 to 39, which of the following could be the width, in inches, of the wooden strip?
I. 1
II. 3
III. 4
I only
II only
I and II only
I and III only
I, II, and III
这题的坑真的是很好,特别容易就掉坑里
假设小正方形面积为X^2,大正方形面积为Y^2
X^2/Y^2-X^2=25/39
则X^2/Y^2=25/64
所以x/y=5/8
wooden strip的宽度是(y-x)/2=3/16y
由于没有说y是整数,所以什么数字都与可能满足条件
Area of brass square/ area of wooden strip = 25 /39
lets say length of the wooden plaque= l and length of the square brass = x
then
x^2 / (l^2 - x^2) = 25/39
=>39x^2 = 25l^2 - 25x^2
=>64x^2 = 25l^2
=>8x = 5l
Width of wooden strip should be l-x
=>x = 5l/8
so l -x = l = 5l/8 = 3l/8
Now 3l/8 could be any value depending on the value of l
相对比例关系不能确定绝对宽度
这题真是醉了,但是也花了些时间是因为不敢相信怎么会有这么没有限制条件的简单题啊
没说一定是整数