sagarsir wrote:
Bunuel wrote:
Instead of walking along two adjacent sides of a rectangular field, Sabrina took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is:
(A) 1:4
(B) 3:8
(C) 1:2
(D) 2:3
(E) 3:4
Preferably look for an option that has diagonal as integer and test t.
OPTION E 3,4,5. Saving = 3+4-5=2 which is half the longer side 4.
Kudos... If you like
Your logic makes perfect sense that you should check for integral diagonal first though note one thing - the actual length of the diagonal NEED NOT be an integer. For example, the actual sides could be 1.5 and 2 such that the diagonal is 2.5 and sum of 1.5 + 2/2 is also 2.5. The sum of one side + half of another side may not be an integer and hence the diagonal may not be an integer.
What is important is that the diagonal must be a
RATIONAL number.
For example, if we test for option (A) 1:4
The diagonal of the rectangle with sides 1 and 4 would be \(\sqrt{17}\). That is an irrational number. This is not possible since the sum of 1 + 4/2 = 3 will be rational.
Only in case of option (E) will we get a RATIONAL diagonal length = 5.
Hence option (E) is correct.
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