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## Geometry and Mensuration: Level 1 Test 4

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*Geometry and Mensuration: Level 1 Test 4*.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%% Your answers are highlighted below.

Question 1 |

In a triangle ΔABC, the side BC is extended up to D. Such that CD= AC, if ∠BAD= 109

^{o}and ACB= 72^{o}then the value of ∠ABC isA | 35 ^{o} |

B | 60 ^{o} |

C | 40 ^{o} |

D | 45 ^{o} |

Question 2 |

The area of a square is 2.25 cm

^{2}. What is its perimeter?A | 9.0 cms |

B | 6.0 cms |

C | 1.5 cms |

D | 4.5 cms. |

Question 3 |

The length of a rectangle is 20% more than its breadth. What will be the ratio of the area of this rectangle to the area of a square whose side is equal to the breadth of the rectangle?

A | 5: 6 |

B | 6: 5 |

C | 2: 1 |

D | Data inadequate |

Question 3 Explanation:

$ \begin{array}{l}The\,\,required\,\,ratio\,\,will\,\,be\,\,1.2\times breadt{{h}^{2}}:breadt{{h}^{2}}=6:5\\Correct\,\,option\,\,is\,\,(b)\end{array}$

Question 4 |

The sum of three altitudes of a triangle is

A | equal to the sum of three sides |

B | less than the sum of sides |

C | greater than the sum of sides |

D | twice the sum at sides |

Question 4 Explanation:

Since the question is based on a geometrical identity it must be valid for all triangles.

Thus we can assume an equilateral triangle of side a cm.

Altitude = √3a/2.

Sum of all altitudes = √3a/2 cm

1.5 X 1.73 a= 2.595a cm

Sum of the three sides = 3a cm.

Thus we can assume an equilateral triangle of side a cm.

Altitude = √3a/2.

Sum of all altitudes = √3a/2 cm

1.5 X 1.73 a= 2.595a cm

Sum of the three sides = 3a cm.

Question 5 |

A rectangular carpet has an area of 120sq. metres and a perimeter of 46 metres. The length of its diagonal (in metres) is:

A | 11 |

B | 13 |

C | 15 |

D | 17 |

Question 5 Explanation:

$ \begin{array}{l}Diagonal=\sqrt{lengt{{h}^{2}}+breadt{{h}^{2}}}\\=\sqrt{{{\left( length+breadth \right)}^{2}}-2\,length\times breadth}\\=\sqrt{{{\left( \frac{46}{2} \right)}^{2}}-2\times 120}=17m\end{array}$

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