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07 Apr 2020, 08:29
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A
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Difficulty:
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61% (01:45) correct
39%
(01:48)
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A parallelogram ABCD has area of 48 cm^2. If the length of CD is 8 cm and that of AD is s cm, then which one of the following is necessarily true?
A. s ≥ 6
B. s ≠ 6
C. 5 ≤ s ≤ 7
D. 4 ≤ s ≤ 6
E. s ≤ 6
Are You Up For the Challenge: 700 Level Questions
A. s ≥ 6
B. s ≠ 6
C. 5 ≤ s ≤ 7
D. 4 ≤ s ≤ 6
E. s ≤ 6
Are You Up For the Challenge: 700 Level Questions
07 Apr 2020, 08:41
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Bunuel
Area of paralello gram = 2* area of triangle ACD = 2* (1/2 * CD*AD*SinD)= CD*AD*SinD =8*s*SinD=48 : s*SinD =6
s=6/SinD the max value of SinD is one and its in the denominator of this expression,
so that means the min value that s can have is 6/1 thus s ≥ 6
OPTION:A
07 Apr 2020, 08:45
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area of parallelogram=a*b*sinC
where a,b are lengths of sides and is C the angle between them
so, a*b*sin C=48
or,8s*sinC=48
or,s*sinC=6
or,sinC=6/s
now, sinC must be ≤1
so, s must be ≥6
correct answer A
where a,b are lengths of sides and is C the angle between them
so, a*b*sin C=48
or,8s*sinC=48
or,s*sinC=6
or,sinC=6/s
now, sinC must be ≤1
so, s must be ≥6
correct answer A
