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Examples of Pythagoras Theorem

Here are few examples of Pythagoras theorem and its application in different situations.

 

1. Find the length of the hypotenuse in the following triangles (all measurements in cm)

a) k2  =  92  +  402  Examples of Pythagoras theorem_1

=  81 + 1600

k  =  sqrt{1681}  =  41 cm

 

b) q2  =  202  +  212  Examples of Pythagoras theorem_2

=  400 + 441

q  =  sqrt{841}  =  29 cm

 

c) s2  =  62  +  82  Examples of Pythagoras theorem_3

=  36 + 64

s  =  sqrt{100}  =  10 cm

 

2. Find as a surd, the exact length of the hypotenuse in each triangle (all measurements are in mm).

a) h2  =  22  +  42Examples of Pythagoras theorem_4

=  4 + 16

h  =  sqrt{20}

=  2sqrt{5} mm

 

b) s2  =  72  +  112  Examples of Pythagoras theorem_5

=  49 + 121

s  =  sqrt{170}  =  13.04 mm

 

c) h2  =  62  +  62  Examples of Pythagoras theorem_6

=  36 + 36

h  =  sqrt{72}

=  sqrt{4~*~3~*~3~*~2}

h  =  6sqrt{2} mm

 

3. Find (correct to 1 decimal place) the length of the hypotenuse in a right-angled triangle whose perpendicular sides have lengths:

a) 2.3 cm, 7.4 cm

c2 = 2.32 + 7.42

c  =  sqrt{5.29~+~54.76}

=  sqrt{60.05}

=  7.7 cm

 

b) 6.7 m, 8.5 m

c2 = 6.72 + 8.52

c  =  sqrt{44.89~+~72.25}

=  sqrt{117.14}

=  10.8 m

 

c) 4.8 mm, 9.6 mm

c2 = 4.82 + 9.62

c  =  sqrt{23.04~+~92.16}

=  sqrt{115.2}

=  10.7 mm