In the Given Figure, Ad = 13 Cm, Bc = 12 Cm, Ab = 3 Cm and Angle Acd = Angle Abc = 90°. Find the Length of Dc. - Mathematics

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Sum

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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Chapter 16: Pythagoras Theorem - Exercise 16

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Selina Concise Mathematics Class 7 ICSE
Chapter 16 Pythagoras Theorem
Exercise 16 | Q 11

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