TRIANGLES (CDS)

Total Questions: 69

61. Consider the following [2014 (II) Evening Shift]

ABC and DEF are triangles in a plane such that AB is parallel to DE, BC is parallel to EF and CA is parallel to FD.
Statement I If ∠ ABC is a right angle, then ∠ DEF is also a right angle.
Statement II Triangles of the type ABC and DEF are always congruent.

Which one of the following is correct in respect of the above statements?

Correct Answer: (c) Statement I is correct and Statement II is incorrect
Solution:


62. The three sides of a triangle are 15, 25, x units. Which one of the following is correct? [2014 (I) Morning Shift]

Correct Answer: (a) 10 < x < 40
Solution:In a triangle, sum of two sides is always greater than third side.
i.e. x < 40 ...(i)
Difference of two sides is always less than third side.
i.e. 10 < x ...(ii)
From Eqs. (i) and (ii),
10 < 40 < x

63. Which one of the following is a Pythagorean triple in which one side differs from the hypotenuse by two units? [2014 (I) Morning Shift]

Correct Answer: (d)
Solution:By hit and trial method,
[(2 × 2), (2)² - 1, (2)² + 1] = (4, 3, 5)
[put n = 2 in option (d)]
which satisfy Pythagoras theorem and one side differs from hypotenuse by 2 units.

64. The sides of a right angled triangle are equal to three consecutive numbers expressed in centimetres. What can be the area of such a triangle? [2014 (I) Morning Shift]

Correct Answer: (a) 6 cm
Solution:Since, the triangle is right angled. So, all the three consecutive sides must satisfy Pythagoras theorem.

65. If triangles ABC and DEF are similar such that 2 AB DE = and BC = 8 cm, then what is EF equal to? [2014 (I) Morning Shift]

Correct Answer: (a) 16 cm
Solution:∆ABC ~ ∆DEF

66. The sides of a triangle are in geometric progression with common ratio r < 1. If the triangle is a right angled triangle, the square of common ratio is given by [2014 (I) Morning Shift]

Correct Answer: (b)
Solution:Let the sides of triangle be a/r, a, ar and since r < 1.

67. In a ∆ABC, AD is perpendicular to BC and BE is perpendicular to AC. Which of the following is correct? [2014 (I) Morning Shift]

Correct Answer: (c) AD × BD = AE × BE
Solution:Two sides of triangle have perpendiculars then AD/AC = BE/BC

68. Let ABC be a triangle right angled at B. If AB= 6 cm and BC=8 cm, then what is the length of the circumradius of the ∆ABC ? [2014 (I) Morning Shift]

Correct Answer: (d) 5 cm
Solution:Given, ∆ABC is right angled at B.

69. If AD is the internal angle bisector of ZA in ∆ABC with AB = 3 cm and AC = 1, then what is BD: BC equal to? [2014 (I) Morning Shift]

Correct Answer: (d) 3 : 4
Solution:In ∆ABC, AD is the internal angle bisector of ∠A.