94 Quadratics (Chapter 3)3 The sum of a natural number and its square is 210. Find the number.
4 The product of two consecutive even numbers is 360. Find the numbers.5 The number of diagonals of ann-sided polygon is given by the formula D=
n
2
(n¡3).A polygon has 90 diagonals. How many sides does it have?
6 The length of a rectangle is 4 cm longer than its width. The rectangle has area 26 cm^2. Find its width.
7 A rectangular box has a square base with sides of lengthxcm. Its height
is 1 cm longer than its base side length. The total surface area of the box
is 240 cm^2.
a Show that the total surface area is given by A=6x^2 +4xcm^2.
b Find the dimensions of the box.8 An open box can hold 80 cm^3. It is made from a square piece
of tinplate with 3 cm squares cut from each of its 4 corners.
Find the dimensions of the original piece of tinplate.Example 27 Self Tutor
Is it possible to bend a 12 cm length of wire to form the perpendicular sides of a right angled triangle
with area 20 cm^2?Suppose the wire is bentxcm from one end.
The area A=^12 x(12¡x))^12 x(12¡x)=20
) x(12¡x)=40 becomes
) 12 x¡x^2 ¡40 = 0
) x^2 ¡ 12 x+40=0
Now ¢=(¡12)^2 ¡4(1)(40)
=¡ 16 which is < 0
There are no real solutions, indicating this situation isimpossible.9 Is it possible to bend a 20 cm length of wire into the shape of a rectangle which has an area of 30 cm^2?
10 The rectangle ABCD is divided into a square and a smaller
rectangle by [XY] which is parallel to its shorter sides.
The smaller rectangle BCXY issimilarto the original rectangle,
so rectangle ABCD is agolden rectangle.The ratio
AB
AD
is called thegolden ratio.Show that the golden ratio is
1+p
5
2
.Hint: Let AB=xunits and AD=1unit.area 20 cm^2
xcm
(-x) 12 ¡¡cmxcm (-x) 12 ¡¡cm
12 cmxcm3 cmABD X CYcyan magenta yellow black(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_03\094CamAdd_03.cdr Friday, 17 January 2014 4:02:37 PM BRIAN