Question

In a right triangle ABC, $∠ B$ = 90°.

1. If AB = 6 cm, BC = 8 cm, find AC
2. If AC = 13 cm, BC = 5 cm, find AB

Answer 1

(a) $\triangle ABC$ is right-angled at $B$.
Therefore, by applying Pythagoras theorem, we obtain
$AC^2 = AB^2 + BC^2$
$AC^2 = (6 cm)^2 + (8 cm)^2$
$AC^2 = (36 + 64) cm^2$
=$100$ $cm^2$
$AC = (\sqrt{100}) cm = (\sqrt{10 × 10}) cm$
$AC = 10 \;cm$

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(b) $\triangle ABC$ is right-angled at $B$.
Therefore, by applying Pythagoras theorem, we obtain
$AC^2 = AB^2+ BC^2$
$(13 cm)^2= (AB)^2+ (5 cm)^2$
$AB^2= (13 cm)^2- (5 cm)^2$
=$(169 - 25) cm^2$
= $144 \;cm^2$
$AB = (\sqrt{144}) cm = (\sqrt{12 × 12}) \,cm$
$AB = 12 \;cm$