AREA AND PERIMETER (CDS)

Total Questions: 116

51. The diameters of two given circles are in the ratio 12 : 5 and the sum of their areas is equal to the area of a circle of diameter 65 cm. What are their radii? [2017 (II) Evening Shift ]

Correct Answer: (d) 30 cm and 12.5 cm
Solution:Let the radius of two circle are12x and 5x

52. Two straight lines AB and AC include an angle. A circle is drawn in this angle which touches both these lines. One more circle is drawn which touches both these lines as well 2as the previous circle. If the area of the bigger circle is 9 times the area of the smaller circle, then what must be the angle A? [2017 (II) Evening Shift ]

Correct Answer: (b) 60°
Solution:


53. An isosceles triangle is drawn outside on one of the sides of a square as base in which a way that the perimeter of the complete figure is 7/6 times the perimeter of the original square. What is the ratio of area of the triangle to the area of the original square? [2017 (II) Evening Shift ]

Correct Answer: (d) 1 : 3
Solution:We have, Perimetre of PDABC = 2y + 3x

54. What is the area of the triangle whose sides are 51cm, 37cm and 20cm? [2017 (II) Evening Shift ]

Correct Answer: (c) 306 square cm
Solution:Area of ∆ABC

55. Segment QR of length r is a tangent at Q to a circle of radius r with centre at P. What is the area of the part of the triangle PQR, which is outside the circular region? [2017 (II) Evening Shift ]

Correct Answer: (b)
Solution:We have, QR is a tangent of length r


56. An arc of a circle subtents an angle π at the centre. If the length ofthe arc is 22 cm, then what is the radius of the circle? (Take π = ²²⁄₇) [2017 (II) Evening Shift ]

Correct Answer: (b) 7 cm
Solution:We know that,

57. If the perimeter of a rectangle is 10 cm and the area is 4 cm², then its length is [2017 (I) Morning Shift]

Correct Answer: (d) 4 cm
Solution:Let l and b the length and breadth of the rectangle respectively.

58. The areas of two circular fields are in the ratio 16 49: . If the radius of the bigger field is 14 m, then what is the radius of the smaller field? [2017 (I) Morning Shift]

Correct Answer: (b) 8 m
Solution:Let r₁ and r₂ be the radius of the circles.

59. If each of the dimensions of a rectangle is increased by 200%, the area is increased by [2017 (I) Morning Shift]

Correct Answer: (d) 800%
Solution:Let the length and width of the rectangle are x and y respectively,


60. Three circles each of radius 3.5 cm touch one another. The areas subtended between them is [2017 (I) Morning Shift]

Correct Answer: (c)
Solution: