Perimeter And Area - 2D Test

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Perimeter And Area - 2D Test - 3

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Question 1
1 / -0

The sides of a rectangular park are in the ratio 3 : 2 and its area is 3,750 m². The cost of fencing it at 50 paisa per metre is:

A
Rs. 312.50

B
Rs. 375

C
Rs. 187.50

D
Rs. 125

Solution

Let the length and the breadth of the rectangular park be 3a and 2a, respectively.
Therefore, (3a) x (2a) = 3750
⇒ 6a² = 3750
⇒ a² = 625
⇒ a = 25 m
Hence, length = 3 x 25 = 75 m and breadth = 2 x 25 = 50 m
Now, perimeter of the rectangular park = 2(Length + Breadth) = 2(75 + 50) = 250 m
Cost of fencing it at the rate of 0.50 per m = 250 x 0.50 = Rs. 125
Question 2
1 / -0

From a circular sheet of paper with radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

A
1 : 3

B
4 : 1

C
3 : 1

D
4 : 3
Question 3
1 / -0

In a triangle ABC, the lengths of the sides AB and AC are 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

A
17.05

B
27.85

C
22.45

D
26.25
Question 4
1 / -0

The sides of a square are increased by 20% and 40%, respectively. The area of the resulting rectangle exceeds the area of the square by:

A
60%

B
66%

C
68%

D
75%
Question 5
1 / -0

A jogging park has two identical circular tracks touching each other and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously from the point where one of the circular tracks touches the smaller side of the rectangular track. A jogs along the rectangular track, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point?

A
3.88%

B
4.22%

C
4.44%

D
4.72%