Suppose the length of each side of a regular hexagon ABCDEF is 2 cm. It T is the mid point of CD, then the length of AT, in cm, is
\(\sqrt{15}\)
\(\sqrt{13}\)
\(\sqrt{12}\)
\(\sqrt{14}\)
The Correct Option is B
Solution and Explanation
Considering a regular hexagon as made of 6 equilateral triangles, a line connecting the farthest vertices of the hexagon can be seen as formed by the sides of two opposite equilateral triangles within the hexagon. Consequently, its length would be twice the length of the side of the hexagon, which in this case is 4 cm.
Given that line \( AD \) divides the hexagon into two symmetrical halves, it bisects angle \( D \), thereby establishing angle \( ADC \) as 60°.
The value of \( AT \) can be determined using the cosine formula:
\[ AT^2 = 4^2 + 1^2 - 2 \times 1 \times 4 \times \cos 60^\circ \] Simplifying the equation: \[ AT^2 = 16 + 1 - 8 \times \frac{1}{2} \] \[ AT^2 = 17 - 4 \] \[ AT^2 = 13 \] Taking the square root of both sides: \[ AT = \sqrt{13} \]
Final Answer:
The correct option is \( \boxed{(B): \sqrt{13}} \).
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Questions Asked in CAT exam
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\(4(x^2 + y^2 + z^2) = a,\)
\(4(x - y - z) = 3 + a.\)
Then $a$ equals ?- CAT - 2024
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Certain codes may, of course, be so widely distributed in a specific language community or culture, and be learned at so early an age, that they appear not to be constructed – the effect of an articulation between sign and referent – but to be ‘naturally’ given. Simple visual signs appear to have achieved a ‘near-universality’ in this sense: though evidence remains that even apparently ‘natural’ visual codes are culture specific. However, this does not mean that no codes have intervened; rather, that the codes have been profoundly naturalized. The operation of naturalized codes reveals not the transparency and ‘naturalness’ of language but the depth, the habituation and the near-universality of the codes in use. They produce apparently ‘natural’ recognitions. This has the (ideological) effect of concealing the practices of coding which are present.- CAT - 2024
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Sentence: Understanding central Asia’s role helps developments make more sense not only across Asia but in Europe, the Americas and Africa.
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- Para Completion