- ABC - PQR and A - ABC-A - PQR-169- If PQ-18 cm and BC-12 cm- then AB and QR are respectively-

The correct option is B 24 cm, 9 cm 16/9=[AB/PQ]^2=[BC/QR]^2 ⇒16/9=[AB/18]^2 and 16/9=[12/QR]^2 ⇒4/3=AB/18 and 4/3=12/QR ...

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Byju's Answer

Standard X

Mathematics

Relation between Areas and Sides of Similar Triangles

Δ ABC ∼Δ PQR ...

Question

$Δ A B C \sim Δ P Q R$ and $\frac{A (Δ A B C)}{A (Δ P Q R)} = \frac{16}{9}$ . If $P Q = 18$ cm and $B C = 12$ cm, then $A B$ and $Q R$ are respectively:

9

cm,

24

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24

cm,

9

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32

cm,

6.75

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13.5

cm,

16

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Solution

The correct option is B $24$ cm, $9$ cm
$\frac{16}{9} = {[\frac{A B}{P Q}]}^{2} = {[\frac{B C}{Q R}]}^{2}$
$\Rightarrow \frac{16}{9} = {[\frac{A B}{18}]}^{2}$ and $\frac{16}{9} = {[\frac{12}{Q R}]}^{2}$
$\Rightarrow \frac{4}{3} = \frac{A B}{18}$ and $\frac{4}{3} = \frac{12}{Q R}$
$\Rightarrow A B = 24$ cm, $Q R = 9$ cm.

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ΔABC∼ΔPQR and A(ΔABC)A(ΔPQR)=169. If PQ=18 cm and BC=12 cm, then AB and QR are respectively:

The correct option is B 24 cm, 9 cm169=[ABPQ]2=[BCQR]2⇒169=[AB18]2 and 169=[12QR]2⇒43=AB18 and 43=12QR⇒AB=24 cm, QR=9 cm.

$Δ A B C \sim Δ P Q R$ and $\frac{A (Δ A B C)}{A (Δ P Q R)} = \frac{16}{9}$ . If $P Q = 18$ cm and $B C = 12$ cm, then $A B$ and $Q R$ are respectively: