AREA AND PERIMETER (CDS)

Total Questions: 116

81. A square and an equilateral triangle have equal perimeter. If the diagonal of the square is 12√2cm, then the area of the triangle is [2015 (II) Evening Shift]

Correct Answer: (d) 64√3 cm²
Solution:Let length of side of square and equilateral triangle be x and y, respectively.

82. A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the radius of the wheel is 30 cm, then the speed of the cycle is [2015 (II) Evening Shift]

Correct Answer: (b) 15.84 km/h
Solution:Radius of wheel = 30 cm

83. There are 437 fruit plants in an orchard planted in rows. The distance between any two adjacent rows is 2 m and the distance between any two adjacent plants is 2 m. Each row has the same number of plants. There is 1 m clearance on all sides of the orchard. What is the cost of fencing the area at the rate of ₹100 per metre? [2015 (II) Evening Shift]

Correct Answer: (b) ₹16800
Solution:There are 437 fruit plants.

84. The circumference of a circle is 100 cm. The side of the square inscribed in the circle is [2015 (II) Evening Shift]

Correct Answer: (c)
Solution:We have, circumference of circle = 2 πr = 100

85. The diameter of a wheel that makes 452 revolutions to move 2 km and 26 dm is equal to [2015 (II) Evening Shift]

Correct Answer: (b)
Solution:1 km = 1000 m , 1 dm = 10 m


86. A square is inscribed in a right triangle with legs x and y and has common right angle with the triangle. The perimeter of the square is given by [2015 (II) Evening Shift]

Correct Answer: (b)
Solution:Let length of the side of square be l.


87. From a rectangular sheet of sides 18 cm and 14 cm, a semi-circular portion with smaller side as diameter is taken out. Then, the area of the remaining sheet will be [2015 (II) Evening Shift]

Correct Answer: (d) 175 cm²
Solution:Diameter of semi-circle = 14 cm

88. ABCD is a square. If the sides AB and CD are increased by 30%, sides BC and AD are increased by 20%, then the area of the resulting rectangle exceeds the area of the square by [2015 (II) Evening Shift]

Correct Answer: (b) 52%
Solution:Let the side of square be x.


89. The area of a trapezium is 336 cm² . If its parallel sides are in the ratio 5 : 7 and the perpendicular distance between them is 14 cm, then the smaller of the parallel sides is [2015 (II) Evening Shift]

Correct Answer: (a) 20 cm
Solution:Let parallel sides of trapezium are 5x and 7x respectively.

90. AB is a line segment of length 2a, with M as mid-point. Semi-circles are drawn on one side with AM, MB and AB as diameter as shown in the figure. A circle with centre O and radius r is drawn such that this circle touches all the three semi-circles. The value of r is [2015 (II) Evening Shift]

Correct Answer: (c) a/3
Solution:Since, two circles touch each other externally if distance between their centres = Sum of their radii