Question 1155671
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The dimensions including the frame are 40 by 60.<br>
With a frame of uniform width x, the dimensions of the painting alone are (40-2x) by (60-2x).<br>
The area of the frame is twice the area of the painting; that means the area with the frame is 3 times the area of the painting alone.<br>
{{{60*40 = 3(60-2x)(40-2x)}}}<br>
Solve using basic algebra....<br>
If a formal algebraic solution is not required, the problem can be solved mentally in a few seconds.<br>
With the frame, the area is 40*60 = 2400.  That is the product of two numbers whose difference is 20 with a product of 2400.<br>
The area of the painting alone is one-third of the total area, which is 800.<br>
With a frame of uniform width, the dimensions of the painting are two numbers whose difference is also 20.<br>
A couple of moments of mental arithmetic find the dimensions of the painting to be 20 by 40.<br>