Photo Frame Perimeter Question

Let the dimensions of the photograph be L*B (L is length and B is breadth)

The photograph has 1 inch wide border on each side so in the dimension of the photograph and the border (1 inch on each side) will become (L+1+1) * (B+1+1) (See attached figure)
So Area = (L+2) * (B+2) = M (Given) ...(1)

Similarly when the Border is 2 inch on each side then Area will become (L+2+2) * (B+2+2) (see attached figure)
=> (L+4) * (B+4) = M + 52 (Given) ...(2)
[(L+2) + 2] * [(B+2) + 2] = M + 52
(L+2)*(B+2) + 2*(L+2) + 2(B+2) + 2*2 = M + 52
(L+2) * (B+2) = M from 1
=> M + 2* (L+2 + B+2) + 4 = M+52
=> 2*(L+B+4) = M + 52 - M - 4
=> 2(L+B+4) = 48
=> L + B + 4 = 24
=> L + B = 20
So, Perimeter = 2*(L+B) = 2*20 = 40 inches

Hope it helps!

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