SSC CGL 24 Aug 2021 Shift 3 Paper

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Question : 60 of 100

Marks: +1, -0

△ A B C

is right angled at

B

and

D

is a point of

B C

such that

B D=5 {cm}

,

A D=13 {cm}

and

A C=37 {cm}

, then find the length of

D C

(in

{cm})

.

25
30
5
35

Solution:

Given,

A C=37 {cm}

,

B D=5 {cm},

A D=13 {cm}

Applying Pythagoras theorem, In

△ A B D

,

(A D)^{2} \;\; =(A B)^{2}+(B D)^{2}

(13)^{2} \;\; =(A B)^{2}+(5)^{2}

(A B)^{2} \;\; =169-25

(A B)^{2} \;\; =144

A B \;\; =12

Again applying Pythagoras theorem in

△ {ABC}

⇒ \;\; (A C)^{2}=(A B)^{2}+(B C)^{2}

⇒ \;\; (37)^{2}=(12)^{2}+(B C)^{2}

⇒ 1369-144=(B C)^{2} ⇒ 1225=(B C)^{2}

⇒ \;\; B C=√{1225}=35 {cm}

⇒ B D+D C=35 ⇒ 5+x=35

⇒ \;\; B C=x=35-5=30 {cm}

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