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ICSE Class 10 Mathematics Question 16 of 28

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Question 65

Given a triangle ABC, and D is a point on BC such that BD = 4 cm and DC = x cm. If ∠BAD = ∠C and AB = 8 cm, then,

(a) prove that triangle ABD is similar to triangle CBA.

(b) find the value of 'x'.

Given a triangle ABC, and D is a point on BC such that BD = 4 cm and DC = x cm. If ∠BAD = ∠C and AB = 8 cm, then. Maths Competency Focused Practice Questions Class 10 Solutions.
Answer

(a) In △ ABD and △ CBA,

⇒ ∠ABD = ∠CBA (Common angle)

⇒ ∠BAD = ∠ACB (Given)

∴ △ ABD ~ △ CBA (By A.A. axiom)

Hence, proved that △ ABD ~ △ CBA.

(b) We know that,

Corresponding sides of similar triangle are proportional.

∴ABBC=BDBA⇒8x+4=48⇒4(x+4)=8×8⇒4x+16=64⇒4x=64−16⇒4x=48⇒x=484= 12 cm.\therefore \dfrac{AB}{BC} = \dfrac{BD}{BA} \\[1em] \Rightarrow \dfrac{8}{x + 4} = \dfrac{4}{8} \\[1em] \Rightarrow 4(x + 4) = 8 \times 8 \\[1em] \Rightarrow 4x + 16 = 64 \\[1em] \Rightarrow 4x = 64 - 16 \\[1em] \Rightarrow 4x = 48 \\[1em] \Rightarrow x = \dfrac{48}{4} = \text{ 12 cm}.

Hence, x = 12 cm.