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3

For each of the following, calculate the value of x.
(a) x cm (b)
x cm 24 cm
12 cm
16 cm 26 cm Smart
Smart

The length of the
2
2
(a) x = 12 + 16 (b) 26 = x + 24 2 hypotenuse can be
2
2
2
2
2
= 144 + 256 x = 26 – 24 2 calculated using the Pol
function. For instance,
= 400 = 676 – 576 Example 3(a),

x = 400 = 100 press Pol( 1 2 ,

= 20 x = 100
= 10 1 6 ) =
4
Calculate the length of PQ in each of the following diagrams. id ou now
(a) (b) S 8 cm Three numbers a, b and c
R 12 cm R 2 2 2
3 cm Q 6 cm that satisfy c = a + b
S Q are known as a
4 cm 15 cm Pythagorean triples (or
triplets). For example,
P (3, 4, 5), (5, 12, 13),
P (7, 24, 25) and so forth.

2
(a) PR = 3 + 4 2 (b) QS = 6 + 8 2
2
2
2
= 9 + 16 = 36 + 64
= 25 = 100
2
2
2
PQ = PR + RQ 2 PS = QS + PQ 2
2
2
2
= 25 + 12 2 PQ = PS – QS 2
2
= 169 = 15 – 100

PQ = 169 = 125

= 13 cm PQ = 125
= 11.18 cm (2 decimal places)
Self Practice 13.1c CHAPTER
1. For each of the following, calculate the value of x. Give your answer correct to two
decimal places if necessary. 13
(a) (b) x cm (c) (d) 1.0 m
x cm 6 cm 9 cm x m
7 cm 25 cm x cm 1.2 m
8 cm
14 cm

297
The Pythagoras’ Theorem

13 TB Math F1.indd 297 11/10/16 12:22 PM