Cambridge International Mathematics

The theorem of Pythagoras (Chapter 8) 179

Example 11 Self Tutor

An equilateral triangle has sides of length 6 cm. Find its area.

The altitude bisects the base at right angles.

) a^2 +3^2 =6^2 fPythagorasg

) a^2 +9=36

) a^2 =27

) a=

p

27 fas a> 0 g

Now, area=^12 £base£height

=^12 £ 6 £

p

27

=3

p

27 cm^2

¼ 15 : 6 cm^2

So, the area is about 15 : 6 cm^2 :

Example 12 Self Tutor

Let SB bexkm.

From the diagram alongside, we see in triangle SAB that

SABb =90o.

x^2 = 112^2 + 134^2 fPythagorasg

) x^2 = 30 500

) x=

p

30 500 fas x> 0 g

) x¼ 175

So, outpost B is 175 km from base station S.

EXERCISE 8C

1 A rectangle has sides of length 8 cm and 3 cm. Find the length of its diagonals.

2 The longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal

is 10 cm, find the dimensions of the rectangle.

3 A rectangle with diagonals of length 20 cm has sides in the ratio 2:1. Find the:

a perimeter b area of the rectangle.

4 A rhombus has sides of length 6 cm. One of its diagonals is 10 cm long. Find the length of the other

diagonal.

5 A square has diagonals of length 10 cm. Find the length of its sides.

acm

6cm

3cm

xkm

134 km

112 km

A

S

B

A helicopter travels from base station S for km to outpost A. It then turns to the

right and travels km to outpost B. How far is outpost B from base station S?

¡¡ 112 90

134

¡ o

¡¡¡¡

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y:\HAESE\IGCSE01\IG01_08\179IGCSE01_08.CDR Wednesday, 17 September 2008 1:47:01 PM PETER