AREA AND PERIMETER (CDS)

Total Questions: 116

21. The angles of a triangle are in the ratio 1 : 1 : 4. If the perimeter of the triangle is k times its largest side, then what is the value of k? [2019 (I) Morning Shift]

Correct Answer: (a)
Solution:The angle of triangle are in the ratio 1 : 1 : 4. Then, two angle are equal


22. The hypotenuse of a right angled triangle is 10 cm and its area is 24 cm². If the shorter side is halved and the longer side is doubled, the new hypotenuse becomes [2019 (I) Morning Shift]

Correct Answer: (c)
Solution:ABC is right angle triangle at B.


23. Consider the following statements : [2019 (I) Morning Shift]

1. The perimeter of a triangle is greater than the sum of its three medians.
2. In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD.

Which of the above statements is/are correct?

Correct Answer: (c) Both 1 and 2
Solution:The perimeter of a triangle is greater than the sum of its three medians.


24. (Questions 24-26) Read the given information carefully and answer the given questions below. [2019 (I) Morning Shift]

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right-angle.
Diagram for questions (24-26)

What is the area of triangle ADC ?

Correct Answer: (a) 126 cm²
Solution:


25. What is the area of quadrilateral ABCD ? [2019 (I) Morning Shift]

Area of quadrilateral ABCD

Correct Answer: (b) 306 cm²

26. What is the difference between perimeter of triangle ABC and perimeter of triangle ADC? [2019 (I) Morning Shift]

Correct Answer: (c) 6 cm
Solution:Difference between perimeter of ∆ABC and ∆ADC.

27. If base and hypotenuse of a right triangle are (u² - v²) and (u² + v²) respectively and the area of the triangle is 2016 square units, then the perimeter of the triangle may be [2018 (II) Evening Shift]

Correct Answer: (b) 288 units
Solution:According to the question, In right angle ∆ABC, Here,

28. A circle is inscribed in an equilateral triangle of side of length e.e. The area of any square inscribed in the circle is [2018 (II) Evening Shift]

Correct Answer: (d) l²/6
Solution:Side of equilateral ∆ABC = l


29. Let S be the parallelogram obtained by joining the mid-points of the parallelogram T. [2018 (II) Evening Shift]

Consider the following statements
1. The ratio of area of T to that S is 2 : 1
2. The perimeter of S is half of the sum of diagonals of T.

Which of the above statements is/are correct?

Correct Answer: (a) 1 only
Solution:Given,


30. The sides of a triangle are 5 cm, 6 cm and 7 cm. The area of the triangle is approximately [2018 (II) Evening Shift]

Correct Answer: (b) 14.7 cm²
Solution:The sides of triangles are 5cm, 6 cm and 7cm respectively