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In the given figure, angle ADB = 90°, AC = AB = 26 cm and BD = DC. If the length of AD = 24 cm; find the length of BC.

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#### Solution

**Given**:

∆ ABC

∠ADB = 90° and AC = AB = 26 cm

AD = 24 cm

**To find :** Length of BC In right angled ∆ ADC

AB = 26 cm, AD = 24 cm

According to Pythagoras Theorem,

(AC)^{2} = (AD)^{2} + (DC)^{2}(26)^{2} = (24)^{2} + (DC)^{2}676 = 576 + (DC)^{2}⇒ (DC)^{2} = 100

⇒ DC =`sqrt100` = 10 cm

∴ Length of BC = BD + DC

= 10 + 10 = 20 cm

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