[問題]GWD28-30

[kaijen]

Q30:
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?

A. 34
B. 36
C. 38
D. 40
E. 42


Ans: D

[kaijen]

設長=X 寬=Y 求周長2(X+Y)
(X+1)(Y+1)=M
(X+2)(Y+2)=M+52
展開得
XY+ (X+Y)+1=M
XY+2(X+Y)+4=M+52
兩式相減
X+Y=49 得周長2(X+Y)=98
請問我哪裡算錯了? 謝謝

[dibert8]

外框面積 M = (X+2)*(Y+2) = XY + 2*(X+Y) + 4
M + 52 = (X+4)*(Y+4) = XY + 4*(X+Y) + 16
=> 52 = 2*(X+Y) + 12
=> 40 = 2*(X+Y)

[livory]

這題意思不太懂耶!
有人可以幫忙解釋一下嘛?
謝謝!