- This is an assessment test.
- These tests focus on geometry and mensuration and are meant to indicate your preparation level for the subject.
- Kindly take the tests in this series with a pre-defined schedule.

## Geometry and Mensuration: Test 23

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Question 1 |

If the medians of two equilateral triangles are in the ratio 1:2 then what is the ratio of their sides?

1: 2 | |

2: 3 | |

3: 2 | |

√3: √2 |

Question 1 Explanation:

$ \displaystyle \begin{array}{l}Median\text{ }of\text{ }an\text{ }equilateral\text{ }triangle=\frac{\sqrt{3}}{2}a\\By\text{ }given\text{ }condition\\\frac{\frac{\sqrt{3}}{2}{{a}_{1}}}{\frac{\sqrt{3}}{2}{{a}_{2}}}=\frac{1}{2}\\\therefore \,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{1}{2}\end{array}$

Question 2 |

The hypotenuse of a right triangle is 3√10 unit. If the smaller side is tripled and the longer side is doubled, new hypotenuse becomes 9√5 unit. What are the lengths of the smaller and longer sides of the right triangle respectively?

5 unit and 9 units | |

5 units and 6 units | |

3 units and 9 units | |

3 units and 6 units |

Question 2 Explanation:

Let the sides be x , y where x<y

x

9x

Solving the two equations

x = 3 and y=9

x

^{2 }+ y^{2 }=(3√10)^{2}= 909x

^{2 }+ 4y^{2 }=(9√5)^{2}= 405Solving the two equations

x = 3 and y=9

Question 3 |

In the figure given above, PQ = QS and QR = RS. If ∠SRQ = 100°, how many degrees is ∠QPS?

40° | |

30° | |

20° | |

15° |

Question 3 Explanation:

Question 4 |

ABC is a right angled triangle, right angled at C and p is the length of the perpendicular from C on AB. If a, b and c are the lengths of the sides BC, AC and AB respectively, then which one of the following is correct?

(a ^{2} + b^{2})p^{2} = a^{2}b^{2} | |

a ^{2} + b^{2} = a^{2}b^{2}p^{2} | |

p ^{2}= a^{2} + b^{2} | |

p ^{2}= a^{2} –b^{2} |

Question 5 |

AB, EF and CD are parallel lines. Given that, EF= 5 cm GC = 10 cm, AB = 15 cm and DC = 18 cm. What is the value of AC?

20 cm | |

24 cm | |

25 cm | |

28 cm |

Question 5 Explanation:

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