TRIANGLES (CDS)

Total Questions: 69

1. Which one of the following is correct in respect of a right angled triangle? [2019 (II) Evening Shift]

Correct Answer: (c) Its orthocentre lies on the triangle
Solution:Orthocentre of a right angle triangle lies on the triangle. It is a property of a right angle triangle.

2. The perimeters of two similar triangles ABC and PQR are 75 cm and 50 cm, respectively. If the length of one side of the triangle PQR is 20 cm, then what is the length of corresponding side of the triangle ABC? [2019 (II) Evening Shift]

Correct Answer: (b) 30 cm
Solution:∆ABC and ∆PQR are two similar triangles.

3. Suppose P Q, and R are the mid-points of sides of a triangle of area 128 cm² . If a triangle ABC is drawn by joining the mid-points of sides of triangle PQR, then what is the area of triangle ABC? [2019 (II) Evening Shift]

Correct Answer: (b) 8 cm²
Solution:

4. let two lines p and a be parallel. Consider two points B and C on the line p and two points D and E on the line q. The line through B and E intersects the line through C and D at A in between the two lines p and q. If AC AD = 4 : 9, then what is the ratio of area of triangle ABC to that of traingle ADE? [2019 (II) Evening Shift]

Correct Answer: (c) 16 : 81
Solution:


5. ABC is a triangle right angled at B. If AB = 5 cm and BC = 10 cm, then what is the length of the perpendicular drawn from the vertex B to the hypotenuse? [2019 (II) Evening Shift]

Correct Answer: (b) 2√5 cm
Solution:


6. Three consecutive integers form the lengths of a right angled triangle. How many sets of such three consecutive integers is/are possible? [2019 (I) Morning Shift]

Correct Answer: (a) Only one
Solution:Three consecutive integers form the lengths of a right-angled triangle.

7. Consider the following inequalities in respect of any triangle ABC: [2019 (I) Morning Shift]

1. AC −  AB < BC
2. BC  −  AC < AB
3. AB −  BC < AC

Which of the above are correct?

Correct Answer: (d) 1, 2 and 3
Solution:Property of triangle Difference of two side of triangle is less than third side of the triangle. Then, all the statement is correct. Option (d) is correct.

8. (Questions 8 and 9) Read the given information carefully and answer the given question below. An equilateral triangle ABC is inscribed in a circle of radius 20√3 cm. [2019 (I) Morning Shift]

What is the length of the side of the triangle?

Correct Answer: (d) 60 cm
Solution:Let length of the side of the triangle = a

9. The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to ? [2019 (I) Morning Shift]

Correct Answer: (c) 20√3 cm
Solution:Centroid of the triangle ABC is at a distance “d ” from the vertex A. All the centres of triangle at one point in equilateral triangle. hen, circumradius of circumcircle is
equal to “d” distance = 20√3 cm Option (c) is correct.

10. A ladder is resting against a vertical wall and its bottom is 2.5 m away from the wall. If it slips 0.8 m down the wall, then its bottom will move away from the wall by 1.4 m. What is the length of the ladder? [2019 (I) Morning Shift]

Correct Answer: (b) 6.5 m
Solution:A ladder is resting against a vertical wall.