Geometry and Mensuration: Level 1 Test 2

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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^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 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: