A square wooden plaque

[joannabanana]

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


A. I only
B. II only
C. III only
D. I and III only
E. I,II and III

[Tani]

Looking at integer values only, the area of the internal square would be a multiple of 25 (say 25n) and therefore a side of that square would be a multiple of 5.

The complete square would be a multiple of 25 (say 25n) plus a multiple of 39 (say 39n) for a total of 64n and the side would be a multiple of eight. The difference would then be a multiple of 3. The width of the wooden strip would be half that, or 1.5 inches.

However, if you are allowed to use fractions any of the values would work. You would simply need to have the sides of the inner square be 5/8 of the side of the outer square.

[goyalsau]

Looking at integer values only, the area of the internal square would be a multiple of 25 (say 25n) and therefore a side of that square would be a multiple of 5.

The complete square would be a multiple of 25 (say 25n) plus a multiple of 39 (say 39n) for a total of 64n and the side would be a multiple of eight. The difference would then be a multiple of 3. The width of the wooden strip would be half that, or 1.5 inches.

However, if you are allowed to use fractions any of the values would work. You would simply need to have the sides of the inner square be 5/8 of the side of the outer square.

Great Work,