Question 8 If - ABC - PQR- and BC-QR-1-3- then ar- PRQ -ar- BCA is equal to A 9 B 3 C 1-3 D 1-9

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Relation between Areas and Sides of Similar Triangles

Question 8 If...

Question

Question 8
If $Δ A B C \sim Δ P Q R, a n d \frac{B C}{Q R} = \frac{1}{3}, t h e n \frac{a r (Δ P R Q)}{a r (Δ B C A)}$ is equal to

(A) 9
(B) 3
(C) $\frac{1}{3}$
(D) $\frac{1}{9}$

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Δ A B C \sim Δ P Q R, a n d \frac{B C}{Q R} = \frac{1}{3}, t h e n \frac{a r (Δ P R Q)}{a r (Δ B C A)}

\frac{1}{3}

\frac{1}{9}

Δ A B C \sim Δ P Q R

\frac{B C}{Q R} = \frac{1}{3}

\frac{a r (Δ P Q R)}{a r (Δ A B C)}

Δ A B C \sim Δ P Q R

\cdot \frac{a r e a Δ A B C}{a r e a Δ P Q R} = \frac{16}{9}

P Q = 18 c m

B C = 12 c m

1. In $Δ A B C$ and $Δ P Q R$ , $\frac{A B}{P Q} = \frac{A C}{P R}, ∠ A = ∠ P$	(a) AA similarity criterion
2. In $Δ A B C$ and $Δ P Q R$ , $∠ A = ∠ P, ∠ B = ∠ Q$	(b) SAS similarity criterion
3. In $Δ A B C$ and $Δ P Q R$ , $\frac{A B}{P Q} = \frac{A C}{P R} = \frac{B C}{Q R}$ $∠ A = ∠ P$	(c) SSS similarity criterion
4. In $Δ A C B, D E \| \| B C$ $\Rightarrow \frac{A D}{B D} = \frac{A E}{C E}$	(d) BPT

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