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In the given figure, AD = 13 cm, BC = 12 cm, AB = 3 cm and angle ACD = angle ABC = 90°. Find the length of DC.

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#### Solution

**Given :**

∆ ACD = ∠ABC = 90°

and AD = 13 cm, BC = 12 cm, AB = 3 cm

**To find :** Length of DC.

**(i)** In right angled ∆ ABC

AB = 3 cm, BC = 12 cm

According to Pythagoras Theorem,

(AC)^{2} = (AB)^{2} + (BC)^{2}

(AC)^{2} = (3)^{2} + (12)^{2}

(AC) =`sqrt(9+144)=sqrt153` cm

**(ii) **In right angled ∆ ACD

AD = 13 cm, AC =`sqrt153`

According to Pythagoras Theorem,

DC^{2} = AB^{2 }− AC^{2}

DC^{2}= 169 − 153

DC = `sqrt16` = 4 cm

∴ Length of DC is 4 cm

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