OG PS-Q175

[FannyHsieh]

A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. If the ratio of the tiled area to the untiled area is 25 to 39, which of the following could be the width, in inches, of the strip?

I. 1
II. 3
III. 4

Ans.: (E) I, II and III

當時在補習班時老師有先講解這一題，解答步驟至y[sup]2[/sup]/x[sup]2[/sup]=25(裡面的)/64(大的)
結果我現在再回來看卻看不懂這個答案要怎麼去解出來以上三個皆可
還煩請高手指點一下，謝謝

[waleaaa]

我的想法是─　(請參考下圖)
首先，假設tiled area(灰方塊)為 25　則總面積為 25 + 39 = 64
所以可知 X : Y = 5 : (8-5) = 5 : 3
因題目沒有其他的限制，所以三個選項皆可成立!