f.1 maths

1.The lengths of the sides of a triangle are in ratio 2:4:5.
a.Ifthe shortest side is 8cm long , find the length of the other sides.
Let x and y be the other two sides,
x:8=4:2
2x=32
x=16
y:8=5:2
2y=40
y=20
Hence, the other two sides are 16, 20,,
b.If their total length is 66 , find the length of each side.
Let a,b and c be the three sides
a:b:c=2:4:5(Given)
a:b=2:4
4a=2b
b=2a
a:c=2:5
5a=2c
c=2.5a
a+b+c=66
a+2a+2.5a=66
5.5a=66
a=12
b=2a
b=24
c=2.5a
c=30
The length of the other sides are 12,24 and 30,,

2.A distance of 2km is represented by 1cm on a map.
a.Find the scale of the map.
The scale on a map
=1:2x100x1,000
=1:200,000,,
b.A pool has an area of 2 cm square on the map. Find its actual area.
Its actual area
=2x200,000x200,000
=2x2kmx2km
=8km square
3.If x> √11 and x is a positive integer , then x can be ?
a.2
b.3
c.3.32
d.4
Since,
2<3<√11 <3.32<4
x is an integer(Given)
x=3.32(rejected)
Hence, x=4
Hence, x can be d.4

4.Which of the following is not a Fibonacci number?
(a).3
(b).4
(c).21
(d).89
see http://episte.math.ntu.edu.tw/people/p_fibonacci/
5.(a)Construct △ABC such that AB＝5cm , BC＝6cm ,CA＝5cm
Draw yourself= =
(b)Construct the perpendicular bisector of BC such that it meet BC at D.
Draw yourself
(c)Does the perpendicular bisector constructer in (Q.b) pass through a ?