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Question
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,
DC2 = AB2 − AC2
DC2= 169 − 153
DC = `sqrt16` = 4 cm
∴ Length of DC is 4 cm
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