SOLUTION: A wooden plaque, square in shape, has a bronze inlay, square in shape, in the center. A wooden strip of uniform width surrounds the bronze square. The ratio of the bronze area to

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Question 1106697: A wooden plaque, square in shape, has a bronze inlay, square in shape, in the center. A wooden strip of uniform width surrounds the bronze square. The ratio of the bronze area to the wooden area is 25 to 39. Calculate width of the wooden strip.
Let x = length of side of plaque.
Let y = length of side of inlay.
Let w = width of wooden strip.

Area of square = s^2.
Area of plaque = x^2.
Area of inlay = y^2.
Not sure how to continue. Non-homework.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
 = 


It is what you are given, according to the condition.


Simplify:

 = ,

 = .


Thus you have this quadratic equation for the RATIO  .


You can solve the equation and find this ratio from there.


Notice that the ratio is  THE ONLY thing  which you can obtain from the given data,


          and  you can not obtain dimensions separately,  because there is NO sufficient data for it.


To get better understanding of this fact, imagine two geometrically similar configurations.

The "ratio correlations" will be the same, but the real/actual dimensions will be different.


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For similar problems, see the lesson
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
in this site.


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