Question

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Answer 1

Using Pythagoras theorem:

AC²-CD²=AD²

√10²-6²

=√100-36

=√64

=8.

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Answer 2

Triangle ACD is a right angled triangle.

Therefore,

Pythagoras Theorem can be applied.

Pythagoras Theorem -

$hypotenuse {}^{2} = height {}^{2} + base {}^{2}$

Hypotenuse = AC = 10 cm

Base = CD = 6 cm

Height = AD = ?

By substituting the values,

${10}^{2} = height {}^{2} + {6}^{2} \\ height {}^{2} = {10}^{2} - {6}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 -36 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 64$

Therefore,

$height = \sqrt{64 } = 8$

Height = 8 cm.

Altitude AD measures 8 cm