Question 1125023
<br>
If x is the uniform width of the border, then the dimensions of the picture are 30-2x by 16-2x.  So algebraically<br>
{{{(30-2x)(16-2x) = 176}}}<br>
You can solve the problem by solving that equation.<br>
But a solution can be found more quickly using logical reasoning and a bit of simple arithmetic.<br>
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.<br>
So find two numbers whose difference is 14 and whose product is 176.<br>
176 = 2*88 no...
176 = 4*44 no...
175 = 8*22 YES!!<br>
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.