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Geometry and Mensuration: Level 1 Test 4
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Question 1 
In a triangle ΔABC, the side BC is extended up to D. Such that CD= AC, if ∠BAD= 109^{o} and ACB= 72^{o} then the value of ∠ABC is
35^{o}  
60^{o}  
40^{o}  
45^{o} 
Question 2 
The area of a square is 2.25 cm^{2}. What is its perimeter?
9.0 cms  
6.0 cms  
1.5 cms  
4.5 cms. 
Question 3 
The length of a rectangle is 20% more than its breadth. What will be the ratio of the area of this rectangle to the area of a square whose side is equal to the breadth of the rectangle?
5: 6  
6: 5  
2: 1  
Data inadequate 
Question 3 Explanation:
$ \begin{array}{l}The\,\,required\,\,ratio\,\,will\,\,be\,\,1.2\times breadt{{h}^{2}}:breadt{{h}^{2}}=6:5\\Correct\,\,option\,\,is\,\,(b)\end{array}$
Question 4 
The sum of three altitudes of a triangle is
equal to the sum of three sides  
less than the sum of sides  
greater than the sum of sides  
twice the sum at sides

Question 4 Explanation:
Since the question is based on a geometrical identity it must be valid for all triangles.
Thus we can assume an equilateral triangle of side a cm.
Altitude = √3a/2.
Sum of all altitudes = √3a/2 cm
1.5 X 1.73 a= 2.595a cm
Sum of the three sides = 3a cm.
Thus we can assume an equilateral triangle of side a cm.
Altitude = √3a/2.
Sum of all altitudes = √3a/2 cm
1.5 X 1.73 a= 2.595a cm
Sum of the three sides = 3a cm.
Question 5 
A rectangular carpet has an area of 120sq. metres and a perimeter of 46 metres. The length of its diagonal (in metres) is:
11  
13
 
15  
17 
Question 5 Explanation:
$ \begin{array}{l}Diagonal=\sqrt{lengt{{h}^{2}}+breadt{{h}^{2}}}\\=\sqrt{{{\left( length+breadth \right)}^{2}}2\,length\times breadth}\\=\sqrt{{{\left( \frac{46}{2} \right)}^{2}}2\times 120}=17m\end{array}$
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