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## Geometry and Mensuration: Level 1 Test 3

Congratulations - you have completed Geometry and Mensuration: Level 1 Test 3. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%%
 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: $\begin{array}{l}The\,\,centroid\,\,divides\,\,the\,\,median\,\,in\,\,the\,\,ratio\,\,2:1.\\Thus,GD=1/3\times 9=3cm.\\BG=2/3\times 6cm=4cm.\\Thus\,\,BD=\sqrt{({{3}^{2}}+{{4}^{2}})}=5\\Correctoptionis(c)\end{array}$
 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: $\displaystyle \begin{array}{l}We\text{ }know\text{ }that\text{ }if\text{ }in\text{ }a\text{ }triangle\text{ }ABC,\text{ }AD\text{ }is\text{ }the\text{ }internal\text{ }bisector,\\\frac{AB}{AC}=\frac{BD}{DC}=\frac{5}{7.5-5}=1:1.15=2:3\end{array}$
 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 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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