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## Geometry and Mensuration: Level 1 Test 2

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Question 1 |

In an isosceles triangle, if the unequal angle is twice that sum of the equal angles, then each equal angle is

A | 120 ^{o} |

B | 60 ^{o} |

C | 30 ^{o} |

D | 90 ^{o} |

Question 1 Explanation:

Let the unequal angle is 4x units and x cm resp.

Thus 4x+2x= 180 => x = 30

Equal angles are equal to 30

Correct option is (c)

Thus 4x+2x= 180 => x = 30

Equal angles are equal to 30

^{o}.Correct option is (c)

Question 2 |

The diameter of a circle is equal to the perimeter of a square whose area is 3136 sq. ems, What is the circumference of the circle?

A | 352 cms. |

B | 704 cms. |

C | 39424 cms. |

D | Cannot be determined |

Question 2 Explanation:

$ \displaystyle \begin{array}{l}The\text{ }side\text{ }of\text{ }the\text{ }square\text{ }=\sqrt{3136}=56cm\\The\text{ }diameter\text{ }of\text{ }circle\text{ }=\text{ }56\times 4\text{ }=\text{ }224cm\\The\text{ }radius\text{ }=\text{ }112\text{ }cm\\Thus\text{ }the\text{ }circumference\text{ }of\text{ }circle\text{ }=2\pi r=704cm\\Correct\text{ }option\text{ }is\text{ }\left( b \right)\end{array}$

Question 3 |

In a triangle ABC, AB= AC, ∠BAC= 40

^{o}then the external angle at B is:A | 90 ^{o} |

B | 70 ^{o} |

C | 110 ^{o} |

D | 80 ^{o} |

Question 3 Explanation:

$ \displaystyle \begin{array}{l}If\,\,BAC=\text{ }{{40}^{o}},\\BAC=BAC=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }\left( {{180}^{o}}-{{40}^{o}} \right)\text{ }=\text{ }{{70}^{o}}\\The\text{ }external\text{ }angle\text{ }of\text{ }B\text{ }=\text{ }180-70\text{ }=\text{ }{{110}^{o}}\\Correct\text{ }option\text{ }is\text{ }\left( c \right)\end{array}$

Question 4 |

If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 192 m

^{2}. What is the area of the original rectangle?A | 184m ^{2} |

B | 196m ^{2} |

C | 204 m ^{2} |

D | None of these |

Question 4 Explanation:

$ \displaystyle \begin{array}{l}The\text{ }new\text{ }rectangle\text{ }is\text{ }\left( 1.2\times 0.8 \right)=0.96\text{ }of\text{ }the\text{ }original\text{ }rectangle.\\The\text{ }new\text{ }rectangl{{e}^{'}}s\text{ }area\text{ }is\text{ }192\text{ }{{m}^{2}}.\\Thus\text{ }the\text{ }old\text{ }rectangl{{e}^{'}}s\text{ }area\text{ }=\frac{192}{0.96}=200{{m}^{2}}\end{array}$

Question 5 |

The sides of a triangle are in ratio 3: 4: 6. The triangle is:

A | acute-angled |

B | right-angled |

C | obtuse-angled |

D | either acute-angled or right-angled |

Question 5 Explanation:

Let the sides be 3,4,6 units resp.

we can see that

3

Thus the triangle is obtuse angled triangle.

Correct option is (c)

we can see that

3

^{2}+4^{2}<6^{2}Thus the triangle is obtuse angled triangle.

Correct option is (c)

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