Geometry and Mensuration: Level 3 Test 2

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Geometry and Mensuration: Level 3 Test 2

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Question 1

An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in digress?

A	75
B	90
C	120
D	150

Question 1 Explanation:

We know that BP=AB and thus since angle PBC = 60^o
Thus angle ABP = 30^o and angle BAP = (180-30)/2 = 75^o
Angle DAP = 90-75 = 15.
Thus angle APD = 180-2x15 = 150⁰
Correct answer is (d)

Question 2

The points of intersection of three lines 2X +3Y -5 =0 5X -7Y +2 = 0 And 9X -5Y -4 =0

A	Form a triangle
B	Are on lines perpendicular to each other
C	Are on lines parallel to each other
D	Are coincident

Question 2 Explanation:

The points of intersection of the three graphs are : (1,1)
( If only two pairs of equations are solved one
can find that only one possible solution exists)
Thus correct option is (d)

Question 3

In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF. AE =22, BE= 6, CF =16 and BF =2. Find the length of the line joining the mid-points of the sides AB and BC.

A	4√2
B	5
C	3.5
D	None of these

Question 3 Explanation:

$\displaystyle \begin{array}{l}The\text{ }length\text{ }of\text{ }the\text{ }line\text{ }joining\text{ }the\text{ }mid\text{ }point\text{ }of\text{ }AB\text{ }and\text{ }BC\text{ }=1/2\text{ }of\text{ }AC\\\sqrt{{{6}^{2}}+{{8}^{2}}}=5cm\end{array}$

Question 4

In the adjoining figure, points A, B, C and D lie on the circle. AD= 24 and BC= 12. What is the ratio of the area of ΔCBE to that of the triangle ΔADE?

A	1: 4
B	1: 2
C	1: 3
D	Data insufficient

Question 4 Explanation:

The area of the triangle is directly proportional to the square of the bases.
Since the ratio of the length = 1:2
Therefore, the area should be in the ratio of 1:4.
Correct option is (a)

Question 5

Below shown are three circles, each of radius 20 and centers at P, Q and R; further AB= 5, CO 10 and EF= 12. What is the perimeter of the triangle PQR?

A	120
B	66
C	93
D	87

Question 5 Explanation:

Now let us consider the circle with center Q.
EQ= 20-EF = 8 and also PE = 8
Similarly PA=BR =20- AB = 15
QO=CR = 20-10 = 10.
The perimeter of the triangle PQR = 2x(8+15+10)+5+10+12 = 93
Correct option is (c)

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