CAT Practice : Coordinate Geometry

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Apply cosine rule!

Side of a triangle

    Q.33: The two sides of a triangle are 8 cm and 9 cm and one angle is 60. Which of the following can be the length of its third side?
    I. cm
    II. cm
    III. (4.5 - ) cm
    IV. (4 + ) cm
    V. (9 + ) cm

    1. Only II and IV
    2. Only I and III
    3. Only I, II and V
    4. Only II, III and IV

 

  • Correct Answer
    Choice (D). Only II, III and IV

Detailed Solution

Case I:
Let x be the side opposite the angle


By cosine rule, x2 = 82 + 92 – 2*8*9*cos 60
x2 = 145 – 72 = 73
or x =

Case II:
Let 9 cm be the side opposite the angle


By cosine rule, 92 = 82 + x2 – 2*8*x*cos 60
17 = x2 - 8x
x2 - 8x - 17 = 0
or x = (8 +- ) / 2
= 4 +-
Only 4 +


Case III:
Let 8 cm be the side opposite the angle


By cosine rule, 82 = 92 + x2 – 2*9*x*cos 60
-17 = x2 - 9x
x2 - 9x + 17 = 0
or x = (9 +- ) / 2
= 4.5 +- ()/2
=4.5 +-





Correct Answer: (D). Only II, III and IV



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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.