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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
120o
B
60o
C
30o
D
90o
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 30o.
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= 40o then the external angle at B is:
A
90o
B
70o
C
110o
D
80o
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 m2.  What is the area of the original rectangle?
A
184m2
B
196m2
C
204 m2
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
32+42<62
Thus the triangle is obtuse angled triangle.
Correct option is (c)
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