Area

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141 The circumference of a circle is equal to the perimeter of a rectangle. The length and the breadth of the rectangle are 45 cm and 43 cm, respectively. What is the half the radius of the circle?

A
56 cm
B
14 cm
C
28 cm
D
7 cm

142 A person observed that he required 30 s time to cross a circular ground along it's diameter than to cover it once along the boundary. If his speed was 30m/min, then the radius of the circular ground is (take 7i = 2$$\frac{2}{7}$$)

A
10.5 m
B
3.5 m
C
5.5 m
D
7.5 m

143 Two circles with radius 2R and √2R intersect each other at points A and B. The centers of both the circles are on the same side of AB. O is the center of the bigger circle and ∠AOB is 60°. Find the area of the common region between two circles:

A
(√3 – π – 1)R2
B
(√3 – π)R2
C
(13π/6 + 1 - √3)R2
D
(13π/6 + √3)R2

144 Points P, Q, R and S are taken on sides AB, BC, CD and DA of square ABCD respectively, so thatAP : PB = BQ : QC = CR : RD = DS : SA = 1 : n . Then the ratio of the area of PQRS to the area of ABCD is:

A
1 : (1 + n)
B
1 : n
C
1 + n2 : (1 + n)2
D
(1 + n ) : (1 + n2)

144 The area of a rectangle is 4 times of the area of a square. The length of the rectangle is 90 cm and the breadth of the rectangle is $$\frac{2}{3}$$ rd of the side of the square. What is the side of the square?

A
10 cm
B
20 cm
C
15 cm
D
Couldn't be determined

145 The length and the breadth of a rectangular plot are in the ratio of 5 : 3. The owner spends ? 3000 for surrounding it from all the sides at the rate of ₹ 7.5 per metre. What is the difference between the length and breadth of the plot?

A
50 m
B
100 m
C
75 m
D
60 m

146 A circle of radius 10 cm has an equilateral triangle inscribed in it. The length of the perpendicular drawn from the centre to any side of the triangle is

A
2.5V3 cm
B
5-J3 cm
C
10V3 cm
D
None of these

147 The area of circle inscribed in an equilateral triangle is 154 sq cm. What is the perimeter of the triangle?

A
21 cm
B
42V3 cm
C
21V3
D
42 cm

148 What is the area between a square of side 10 cm and two inverted semicircular, cross-sections each of radius 5 cm inscribed in the square?

A
17.5 cm2
B
18.5 cm2
C
20.5 cm2
D
21.5 cm2

149 The base of a parallelogram is thrice of it's height. If the area of the parallelogram is 2187 sq cm, find it's height:

A
27 cm
B
35 cm
C
29 cm
D
26 cm

150 In a trapezium, the two non-parallel sides are equal in length, each being of 5 unit's. The parallel sides are at a distance of 3 unit's apart. If the smaller side of the parallel sides is of length 2 unit's, then the sum of the diagonals of the trapezium is

A
10V5 unit's
B
6V5 unit's
C
5V5 unit's
D
3V5 unit's