I know it might be the dumbest question on this website but I cannot understand why the area of the picture (96) is multiplied by 2 while estimating the area of the frame for which the question states that both the areas (picture and frame) are same?

Thank you so much for timely reponse.
But here is how I am confused with taking twice the area of a picture for frame's area calculation.
Area of picture = 8×12 = 96
Area of frame is equal to area of picture (given in question). So, area of frame should be equal to picture's area (96)
Area of picture + area of frame = 96 + 96 = 192 (fair enough BUT isnt this an area of picture as well as frame whereas our intention is to write the equation for frame's area ONLY?

Posted from my mobile device

Hi,

We want to find the width of the frame and that can be found only if we take the whole area into consideration.

As the frame width, \(x\) is the same throughout, we can get its value by using the equation given in the solution above.

Hi, I am a bit confused here. How did we get \((8 + 2x)(12 + 2x)\)

Thank you in advanced

see above https://gre.myprepclub.com/forum/the-di ... tml#p66435 the explanation by KarunMendiratta

Call the uniform width x, and the outer dimensions of the picture together with the frame become 8 + 2x and 12 + 2x, because the frame’s width adds to both the top and bottom and the left and right of the picture. The full area of the picture together with frame is then (8 + 2x)(12+ 2x) = 96 + 16x + 24x + 4x^2 = 4x^2 + 40x + 96. This expression must equal 2 × 8 × 12 = 192, because the frame’s area is equal to the picture’s, implying that the area enclosed by the frame and picture together must equal twice the area of the picture alone. So 4x^2 + 40x + 96 = 192. Subtract 192 to obtain 4x^2 + 40x – 96 = 0, and divide by 4 on both sides: x^2 + 10x – 24 = 0.

The left side factors as (x + 12)(x – 2), since 12x – 2x = 10x, and so x = 2 or –12. Only x = 2, (D), works in context of the problem, because a length cannot be negative. You can also get this result using a trial and error approach with the answer choices. When x = 2, the outer dimensions become 12 × 16, for a total area of 192. This makes the picture’s area, 8 × 12 = 96, the same as the frame’s area, 192 – 96 = 96

see above https://gre.myprepclub.com/forum/the-di ... tml#p66435 the explanation by KarunMendiratta

Please refer to the figure below;

Length of Frame = 12 + 2w
Width of Frame = 8 + 2w

Area of Picture = (12)(8)

Area of Frame = (Length of frame)(Width of Frame) - Area of picture
i.e. Area of Frame = (12 + 2w)(8 + 2w) - (12)(8)

Given,
Area of Picture frame = Area of Frame
(12)(8) = (12 + 2w)(8 + 2w) - (12)(8)
(12 + 2w)(8 + 2w) = 2(12)(8)