# Area

## Area

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Question 1 |

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

15360 | |

153600 | |

30720 | |

307200 |

Question 1 Explanation:

Perimeter = Distance covered in 8 min. =(12000/60)x 8m = 1600 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m2.

Question 2 |

An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

2% | |

2.02% | |

4% | |

4.04% |

Question 2 Explanation:

100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm^2.
(A2 - A1) = [(102)2 - (100)2]= (102 + 100) x (102 - 100)= 404 cm^2.
Percentage error =(404/(100 x 100))x 100% = 4.04%

Question 3 |

The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

16 cm | |

18 cm | |

24 cm | |

Data inadequate |

Question 3 Explanation:

(2(l + b))/b=5/1 ==> 2l + 2b = 5b ==> 3b = 2l ==>b=2/3l
Then, Area = 216 cm^2
l x b = 216
l x(2/3)l= 216 ==>l^2 = 324 ==> l = 18 cm.

Question 4 |

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

2.91 m | |

3 m | |

5.82 m | |

None of these |

Question 4 Explanation:

Area of the park = (60 x 40) m2 = 2400 m^2.
Area of the lawn = 2109 m^2.
Area of the crossroads = (2400 - 2109) m2 = 291 m^2.
Let the width of the road be x metres. Then,
60x + 40x - x^2 = 291 ==> x^2 - 100x + 291 = 0 ==> (x - 97)(x - 3) = 0
==> x = 3.

Question 5 |

What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?

814 | |

820 | |

840 | |

844 |

Question 5 Explanation:

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm^2.
Required number of tiles =(1517 x 902)/(41 x 41)= 814.

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