Question

6. In a right triangle ABC, right angled at B, find AC,
if (i) AB = 10 cm. BC = 24 cm
(ii) AB = 7 cm, BC = 24 cm​

Answer 1

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Answer 2

Given :

• A right triangle ABC, right angled at B .
• (i) AB = 10 cm. BC = 24 cm .
• (ii) AB = 7 cm, BC = 24 cm .

To Find :

• Length of AC .

Solution :

(i) AB = 10 cm. BC = 24 cm :

Using Pythagoras Theorem :

$\longmapsto\tt{{(AC)}^{2}={(AB)}^{2}+{(BC)}^{2}}$

$\longmapsto\tt{{(AC)}^{2}={(10)}^{2}+{(24)}^{2}}$

$\longmapsto\tt{{AC}^{2}=100+576}$

$\longmapsto\tt{{AC}^{2}=676}$

$\longmapsto\tt{AC=\sqrt{676}}$

$\longmapsto\tt\bf{AC=26\:cm}$

(ii) AB = 7 cm, BC = 24 cm :

Using Pythagoras Theorem :

$\longmapsto\tt{{(AC)}^{2}={(AB)}^{2}+{(BC)}^{2}}$

$\longmapsto\tt{{(AC)}^{2}={(7)}^{2}+{(24)}^{2}}$

$\longmapsto\tt{{AC}^{2}=49+576}$

$\longmapsto\tt{{AC}^{2}=625}$

$\longmapsto\tt{AC=\sqrt{625}}$

$\longmapsto\tt\bf{AC=25\:cm}$