7.In a right triangle ABC, ∠B =\( 90^{\circ}\).
(a) If AB = 6 cm, BC = 8 cm, find AC

(b) If AC = 13 cm, BC = 5 cm, find AB

(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.