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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.