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Geometry and Mensuration: Level 1 Test 3

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Question 1
Two medians AD and BE of ΔABC intersect at G at right angles. If AD= 9 cm and BE= 6 cm, then the length of BD, in cm, is
A
10
B
6
C
5
D
3
Question 1 Explanation: 
68
$ \begin{array}{l}The\,\,centroid\,\,divides\,\,the\,\,median\,\,in\,\,the\,\,ratio\,\,2:1.\\Thus,GD=1/3\times 9=3cm.\\BG=2/3\times 6cm=4cm.\\Thus\,\,BD=\sqrt{({{3}^{2}}+{{4}^{2}})}=5\\Correctoptionis(c)\end{array}$
Question 2
The length of rectangular plot is thrice its breadth. If the area of the rectangular plot is 6075 sq. metres, what is its length?
A
145 metres
B
130 metres
C
75 metres
D
None
Question 2 Explanation: 
Let the length be 3x m and thus the breadth = x m.
3x2=6075
=> x= 45 m.
Thus length = 45X3 = 135 m
Question 3
In ΔABC, AD is the internal bisector of ∠A, meeting the side BC at D. If BD= 5 cm, BC= 7.5 cm, then AB: AC is
A
2: 3
B
1: 2
C
4: 5
D
3: 5
Question 3 Explanation: 
69
$ \displaystyle \begin{array}{l}We\text{ }know\text{ }that\text{ }if\text{ }in\text{ }a\text{ }triangle\text{ }ABC,\text{ }AD\text{ }is\text{ }the\text{ }internal\text{ }bisector,\\\frac{AB}{AC}=\frac{BD}{DC}=\frac{5}{7.5-5}=1:1.15=2:3\end{array}$
Question 4
A wall 3m × 2.7m × 0.2m of concrete weight 320 kg per cubic meter. What will be the total weight of the wall in kg.?
A
5184.0
B
51.84
C
518.4
D
51840.
Question 4 Explanation: 
Volume of the wall = 3 x 2.7 x 0.2 = 1.62 cu m.
Total weight = 320 X 1.62 = 518.4 Kg.
Question 5
If the circumcentre of a triangle lies outside it, then the triangle is
A
Equilateral
B
Acute angled
C
Right angled
D
Obtuse angled
Question 5 Explanation: 
If the circumcentre is outside the triangle, the triangle must be obtuse.
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