length plus width equals price, factoring?

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im trying to grasp what this means as I usually work with areas (L x W = A) or perimeters (2L + 2W = P)... This problems was presented to me by a colleague and i'm just trying to wrap my head around it. Its about factoring a price of a shape, so one is 75.5 x 57 cm and worth 45,000—and another is 45.5 x 45.5 cm without a price. Normally, I found the price per sqcm of the first one and applied that to the second but was told this was wrong and to find the factor in this case I had to use this formula:

D= Dimension
P= Price
F= Factor

Original
(L + W = D)
75.5 + 57 = 132,5

(P / D = F)
€45.000 / 132,5 = 339,622642

New
(L + W = D)
45.5 + 45.5 = 91

(D x F = P
91 x 339,622642 = €30.905,6604

I probably missed something but what is this function called? Missing the logic here...