- 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 | |

âˆš3: âˆš2 |

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 3âˆš10 unit. If the smaller side is tripled and the longer side is doubled, new hypotenuse becomes 9âˆš5 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 }=(3âˆš10)^{2}= 909x

^{2 }+ 4y^{2 }=(9âˆš5)^{2}= 405Solving the two equations

x = 3 and y=9

Question 3 |

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

40Â° | |

30Â° | |

20Â° | |

15Â° |

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} â€“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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