GreenlightTestPrep wrote:
A project requires a rectangular sheet of cardboard satisfying the following requirement: When the sheet is cut into identical rectangular halves, each of the resulting rectangles has the same ratio of length to width as the original sheet. Which of the following sheets comes closest to satisfying the requirement?
(A) A sheet measuring 7 inches by 10 inches
(B) A sheet measuring 8 inches by 14 inches
(C) A sheet measuring 10 inches by 13 inches
(D) A sheet measuring 3 feet by 5 feet
(E) A sheet measuring 5 feet by 8 feet
So, when you half a rectangle, one side will get halved and other will remain the same.
Thus the ratio of B:L should be same as L/2:B or L:2B..
This means B:L=L:2B or \(L^2=2B^2\)..
Let us check the options with this.
(A) A sheet measuring 7 inches by 10 inches
B=7 and L=10, so \(L^2=2B^2...10^2=2*7^2....100=98\)..YES almost equal
(B) A sheet measuring 8 inches by 14 inches
B=8 and L=14, so \(L^2=2B^2...14^2=2*8^2....196=128\)..NO
(C) A sheet measuring 10 inches by 13 inches
B=10 and L=13, so \(L^2=2B^2...13^2=2*10^2....169=200\)..NO
(D) A sheet measuring 3 feet by 5 feet
B=3 and L=5, so \(L^2=2B^2...5^2=2*3^2....25=18\)..NO
(E) A sheet measuring 5 feet by 8 feet
B=5 and L=8, so \(L^2=2B^2...8^2=2*5^2....64=50\)..NO
A