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Answer :
(a) In right triangle ABC
\(AC^2 = AB^2 + BC^2\quad\) [By Pythagoras Theorem]
\(\Rightarrow AC^2 = (6)^2 + (8)^2 = 36 + 64 = 100\)
\(\Rightarrow AC = \sqrt{100} = 10\)
So we have, AC = 10 cm.
(b) In right triangle ABC
\(AC^2 = AB^2 + BC^2\quad\) [By Pythagoras Theorem]
\(\Rightarrow (13)^2 = AB^2 + (5)^2 \)
\(\Rightarrow 169 = AB^2 + 25\)
\(\Rightarrow 169 – 25 = AB^2\)
\(\Rightarrow 144 = AB^2\)
\(AB = \sqrt{144} = 12 cm\)
So we have, AB = 12 cm.