- 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 25

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Question 1 |

R and S are two points on the sides PT and QT respectively of ΔPQR such that RS= 18 cm, TS= 5 cm and ÐRST= 90

^{o}. If tan ÐPQR= 3.6, then PT: TR =QT: 2 TS | |

2 TS: QT | |

2 QT: TS | |

TS: 2 QT |

Question 1 Explanation:

$ \displaystyle \begin{array}{l}\angle \,RST={{90}^{o}}\\RS=18\,cm\\TS=5\,cm\\\therefore \,\,\tan \,T=\frac{RS}{TS}=\frac{18}{5}=3.6\\\tan \,\angle PQR=3.6\\\therefore \angle T=\angle Q\\\therefore PT=PQ\\\angle T+\angle R={{90}^{o}}\\\Rightarrow 2\,\angle T+2\,\angle R={{180}^{o}}\\\angle T+\angle P+\angle Q={{180}^{o}}\\\Rightarrow \,2T+\angle P={{180}^{o}}\\\therefore \,\,\angle P=2\,\angle R\\\therefore \,\frac{PT}{TQ}=\frac{2TR}{TS}\end{array}$

Question 2 |

BL and CM are medians of ΔABC right-angled at A and BC= 5cm. If BL = 8cm, then the length of CM is

√61/2cm | |

√48/2cm | |

10√2cm | |

4 cm |

Question 3 |

ABCD is a rectangle where the ratio of the lengths of AB and BC is 3: 2. If P is the mid-point of AB, then the value of sin ∠CPB is

3/5 | |

2/5 | |

3/4 | |

4/5 |

Question 4 |

PQRS is a square, T is the mid-point of PQ and M is the mid-point of QR. PM and ST are joined and they meet at L. Then which of the following is correct?

TP: TL= 1: 2 | |

PM = TS | |

∠PMS = ∠PMQ | |

∠PTS = ∠QPM |

Question 5 |

If the sums of the interior angles of a regular polygon be 1080

^{o}, the number of sides of the polygon is6 | |

8 | |

10 | |

12 |

Question 5 Explanation:

Let the number of sides be x.

180(x-2)= 1080,

=> x - 2 = 6=> x = 8

Thus the correct option is (b)

180(x-2)= 1080,

=> x - 2 = 6=> x = 8

Thus the correct option is (b)

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