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Geometry and Mensuration: Level 2 Test 6

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Question 1
$ \displaystyle The\text{ }points\,\left( 0,\frac{8}{3} \right),\,\,\left( 1,\,\,3 \right)\,\,\,and\,\,\,\left( 82,\,\,30 \right),are\text{ }the\text{ }vertices\text{ }of$
A
An obtuse angled triangle
B
An right angled triangle
C
An isosceles triangle
D
None of the Above
Question 1 Explanation: 
$ \begin{array}{l}Since\text{ }the\text{ }third\text{ }point\text{ }is\text{ }a\text{ }large\text{ }distance\text{ }away\text{ }\\from\text{ }the\text{ }other\text{ }two\text{ }and\text{ }the\text{ }other\text{ }two\text{ }are\text{ }relatively\text{ }closer.\text{ }\\It\text{ }cannot\text{ }be\text{ }a\text{ }right\text{ }angle\text{ }and\text{ }isosceles\text{ }triangle.\\{{a}^{2}}=\left\{ {{\left( 0-1 \right)}^{2}}+{{\left( \frac{8}{3}-3 \right)}^{2}} \right\}=\frac{10}{9}=1.11\\{{b}^{2}}=\left\{ {{\left( 82-1 \right)}^{2}}+{{\left( 30-3 \right)}^{2}} \right\}=7290\\{{c}^{2}}=\left\{ {{\left( 82-0 \right)}^{2}}+{{\left( 30-\frac{8}{3} \right)}^{2}} \right\}=7471.11\\it\,\,shows\,\,that\,\,{{c}^{2}}>{{a}^{2}}+{{b}^{2}}\end{array}$
Question 2
A triangle has two of its angles in the ratio of 1: 2. If the measure of one of its angles Is 30 degrees. what is the measure of the largest angle of the triangle In degrees?
A
100
B
90
C
135
D
Cannot be determined
Question 2 Explanation: 
Correct option is (d) as nothing is mentioned whether the angle given is one of the angle which follows the ratio or not.
Question 3
A well with 14m inside diameter is dug 10m deep. Earth taken out of it, has been evenly spread all around it to a width of 21m to form an embankment. The height (in meters) of the embankment is:
A
$ \displaystyle \frac{1}{2}$
B
$ \displaystyle \frac{2}{3}$
C
$ \displaystyle \frac{3}{4}$
D
$ \displaystyle \frac{3}{5}$
Question 3 Explanation: 
Radius = 7 m. and the height = 10 m.
The total volume = Πr2h = 22/7 x 7 x7 x10 = 1540m3
The area of the spread = 22/7(282-72) =2310 m2
The height = 1540/2310 = 2/3
Correct option is (b)
Question 4
The area of a square of side 8 cm Is equal to a rectangle. Which of the following statement/ is/ are can be definitely true about the rectangle?
A
The length of rectangle is 16 times its breadth
B
The length of rectangle is 32 times its breadth
C
The breadth of rectangle is 1/6th of its length
D
The breadth of rectangle is 1/9
Question 4 Explanation: 
The area of Square = 64 sq. cm.
Thus when we factorize 64 ,
we find that in all cases only a is true.
Question 5
In ΔABC, points P, Q and R are the mid-points of sides AB, BC and CA respectively. If area of ΔABC, is 20 sq. units, find the area of ΔPQR.
A
10 sq. units
B
5√3 sq. units
C
5 sq. units
D
None of these
Question 5 Explanation: 
When we joint the midpoints of all sides the half length of the third side will be equal to the line made by joining the midpoints of another two sides
Therefore the area of PQR = ¼ the area of ABC = 5 sq. units
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