Algebraic Solution

Say the original sheet measures L by W, with L > W, so that the cut yields two rectangular halves measuring L/2 by W each.

Per the project requirements, the ratio of these new dimensions must be the same as the ratio of L to W. Consider both possible ways in which the ratio might be set up. If the ratio of original to new is set up as L : W = L/2 : W, then it reduces to 1 = 1/2, an impossible condition. (Or, if you prefer to reason theoretically, it is impossible to reduce L by half but leave W unchanged and have the ratio stay the same.)

Therefore, the width (W) of the original rectangle, must become the longer side for the smaller rectangles. The ratio must be set up as L : W = W : L/2.

Set up the ratio:

\(L/W = 2L/W\)

L/W= 1.4 ( \(Root 2 = 1.4\))

The condition thus requires original dimensions that come as close as possible to satisfying , or, equivalently, .

The one closest to 1.4 is the correct answer.

(A) 10/7 = approximately 1.4

(B) 14/8 = 7/4 = 1.75

(C) 13/10 = 1.3

(D) 5/3 = = approximately 1.7

(E) 8/5 = = 1.6

Choice A comes closest to the requirement. The correct answer is (A).

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we shall fight on the landing grounds,

we shall fight in the fields and in the streets,

we shall fight in the hills;

we shall never surrender!