Geometry and Mensuration: Level 2 Test 3

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Geometry and Mensuration: Level 2 Test 3

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Question 1

The length of the three sides of a right angled triangle are (x–2) cm, x cm and (x+2) cm respectively. Then the value of x is

A	10
B	8
C	4
D	0

Question 1 Explanation:

The longest side = x+2 cm.
Thus,
(x+2)²= x²+ (x-2)²
x² + 4x + 4 = x² + x² + 4 – 4x
x²= 8x
=> x =8

Question 2

ABC is an isosceles triangle with AB= AC. The side BA is produced to D such that AB= AD. IfABC= 30^o , then BCD is equal to

A	45^o
B	90^o
C	30^o
D	60^o

Question 2 Explanation:

CAD = 30 + 30 = 60
Now AD = AC
Thus ACD = (180 – 60)/2 = 60⁰
BCD = 30 + 60 = 90⁰

Question 3

If the height of a triangle is decreased 20% and its base is increased by 20% what will be the effect on its area?

A	No change
B	4% decrease
C	12% decrease
D	16% increase

Question 3 Explanation:

Let the height be h cm and base be b cm.
The area of the triangle = ½ hb
The new height = 0.8h and base = 1.2b
The area of new triangle = 0.8 x 1.2 = 0.96 hb

Question 4

A circular ground whose diameter is 35 metres, has a 1.4 metre broad garden around it. What is the area of the garden in square metres?

A	160.16
B	6.16
C	1122.66
D	Data inadequate

Question 4 Explanation:

The radius = 17.5 m.
The area of the garden is Π(17.5 + 1.4)² – Π17.5²= 160.01
The correct option is (a)

Question 5

2 metres broad pathway is to be constructed around a rectangular plot. The area of the plot is 96 sq. m. The cost of construction is Rs.50 per sq. metre. Then find the total cost of production?