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In ABC,ABC,...

Question

In $△ A B C, A B C, A P Q$ and $¯ ¯¯¯¯¯¯ ¯ P Q ∥ ¯ ¯¯¯¯¯¯ ¯ B C$ . If $P Q = 5, A P = 4, A B = 12$ , then $B C =$ _____

9.6

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20

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15

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5

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Solution

The correct option is C $15$
$I n Δ A P Q a n d Δ A B C$
$P Q | | B C$
$∠ A = ∠ A (c o m m o n)$
$∠ A P Q = ∠ A B C (C o r r e s p o n d i n g a n g l e s)$
$∠ A Q P = ∠ A C B (C o r r e s p o n d i n g a n g l e s)$
$H e n c e b y A A A s i m i l a r i t y$
$Δ A P Q a n d Δ A B C a r e s i m i l a r$
$H e n c e$
$\frac{A P}{A B} = \frac{P Q}{B C}$
$\Rightarrow \frac{4}{12} = \frac{5}{B C}$
$\Rightarrow B C = \frac{12 \times 5}{4}$
$= 15$

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Similar questions

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In △ABC,ABC,APQ and ¯¯¯¯¯¯¯¯PQ∥¯¯¯¯¯¯¯¯BC. If PQ=5,AP=4,AB=12, then BC=_____

The correct option is C 15 InΔAPQandΔABC PQ||BC ∠A=∠A(common) ∠APQ=∠ABC(Correspondingangles) ∠AQP=∠ACB(Correspondingangles) HencebyAAAsimilarity ΔAPQandΔABCaresimilar Hence APAB=PQBC ⇒412=5BC ⇒BC=12×54 =15

In $△ A B C, A B C, A P Q$ and $¯ ¯¯¯¯¯¯ ¯ P Q ∥ ¯ ¯¯¯¯¯¯ ¯ B C$ . If $P Q = 5, A P = 4, A B = 12$ , then $B C =$ _____