SOLUTION: A picture frame measures 16cm by 30cm on the outside, and 176cm^2 of picture shows.fine the uniform width of the frame around the picture

Question 1125023: A picture frame measures 16cm by 30cm on the outside, and 176cm^2 of picture shows.fine the uniform width of the frame around the picture
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

If x is the uniform width of the border, then the dimensions of the picture are 30-2x by 16-2x. So algebraically

You can solve the problem by solving that equation.

But a solution can be found more quickly using logical reasoning and a bit of simple arithmetic.

The difference between the dimensions of the whole frame is 14cm; with a uniform border, the difference between the dimensions of the picture will be 14 cm.

So find two numbers whose difference is 14 and whose product is 176.

176 = 2*88 no...
176 = 4*44 no...
175 = 8*22 YES!!

The dimensions of the picture are 8 by 22; the outer dimensions of the frame are 16 by 30. The differences between the corresponding dimensions are 8cm; that means the uniform border is 4cm wide.
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