Mathematics

In figure given below, AB = 12 cm, AC = 13 cm, CE = 10 cm and DE = 6 cm. Calculate the length of BD.

Pythagoras Theorem

ICSE

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Answer

In right angle △ABC,

By pythagoras theorem,

⇒ AC² = AB² + BC²

⇒ 13² = 12² + BC²

⇒ BC² = 13² - 12²

⇒ BC² = 169 - 144 = 25

⇒ BC = $\sqrt{25}$ = 5 cm.

In right angle △CDE,

By pythagoras theorem,

⇒ CE² = CD² + DE²

⇒ 10² = CD² + 6²

⇒ CD² = 10² - 6²

⇒ CD² = 100 - 36 = 64

⇒ CD = $\sqrt{64}$ = 8 cm.

From figure,

BD = BC + CD = 5 + 8 = 13 cm.

Hence, BD = 13 cm.

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