Geometry question about common areas

studying for an exam in a few days fwi

theres a picture surrounded by a frame. the dimensions of the photo is 25cm by 20. what are the dimensions of the frame if the area of the border surrounding the photo has the same area as the photo itself.

Just what are the dimensions of one rectangle on top of the other.

sorry if your reading this again como

If the border is uniform and of width B then the frame (including the picture) has dimensions (25 + 2B) and (20 + 2B)
The area of the frame only = (25 + 2B)(20 + 2B) - (25 x 20) = 500 + 90B + 4B² - 500 = 4B² + 90B
but this is required to be the same area as the picture then,
4B² + 90B = (25 x 20) = 500...........which we can restructure as :-
4B² + 90B - 500 = 0........................and using the quadratic formula gives :-
B = 4.6107 (we can ignore the negative result as the required dimension is positive)

The outer dimensions of the frame are [25 + (2x4.6107)] by [20 + (2x4.6107)] = 34.22 cm by 29.22 cm and, as we know, the inner dimensions are 25 by 20.

Check : 34.22 x 29.22 ≅ 1000 made up from area of frame itself (500), and area of picture (500).