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Geometry and Mensuration: Test 23
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Question 1 
If the medians of two equilateral triangles are in the ratio 1:2 then what is the ratio of their sides?
1: 2  
2: 3
 
3: 2  
√3: √2 
Question 1 Explanation:
$ \displaystyle \begin{array}{l}Median\text{ }of\text{ }an\text{ }equilateral\text{ }triangle=\frac{\sqrt{3}}{2}a\\By\text{ }given\text{ }condition\\\frac{\frac{\sqrt{3}}{2}{{a}_{1}}}{\frac{\sqrt{3}}{2}{{a}_{2}}}=\frac{1}{2}\\\therefore \,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{1}{2}\end{array}$
Question 2 
The hypotenuse of a right triangle is 3√10 unit. If the smaller side is tripled and the longer side is doubled, new hypotenuse becomes 9√5 unit. What are the lengths of the smaller and longer sides of the right triangle respectively?
5 unit and 9 units  
5 units and 6 units  
3 units and 9 units  
3 units and 6 units 
Question 2 Explanation:
Let the sides be x , y where x<y
x^{2 }+ y^{2 }=(3√10)^{2} = 90
9x^{2 }+ 4y^{2 }=(9√5)^{2} = 405
Solving the two equations
x = 3 and y=9
x^{2 }+ y^{2 }=(3√10)^{2} = 90
9x^{2 }+ 4y^{2 }=(9√5)^{2} = 405
Solving the two equations
x = 3 and y=9
Question 3 
In the figure given above, PQ = QS and QR = RS. If ∠SRQ = 100°, how many degrees is ∠QPS?
40°  
30°  
20°  
15° 
Question 3 Explanation:
Question 4 
ABC is a right angled triangle, right angled at C and p is the length of the perpendicular from C on AB. If a, b and c are the lengths of the sides BC, AC and AB respectively, then which one of the following is correct?
(a^{2} + b^{2})p^{2} = a^{2}b^{2}  
a^{2} + b^{2} = a^{2}b^{2}p^{2}  
p^{2}= a^{2} + b^{2}  
p^{2}= a^{2} –b^{2} 
Question 5 
AB, EF and CD are parallel lines. Given that, EF= 5 cm GC = 10 cm, AB = 15 cm and DC = 18 cm. What is the value of AC?
20 cm  
24 cm  
25 cm  
28 cm

Question 5 Explanation:
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