Question : Let $ riangle {ABC} \sim riangle {RPQ}$ and $\frac{\operatorname{ar}( riangle A B C)}{\operatorname{ar}( riangle P Q R)}=\frac{4}{9}$. If ${AB}=3 {~cm}, {BC}=4 {~cm}$ and ${AC}=5 {~cm}$, then ${PQ}$ (in ${cm}$ ) is equal to:
Option 1: 12
Option 2: 4.5
Option 3: 5
Option 4: 6

Question

Question : Let $ riangle {ABC} \sim riangle {RPQ}$ and $\frac{\operatorname{ar}( riangle A B C)}{\operatorname{ar}( riangle P Q R)}=\frac{4}{9}$. If ${AB}=3 {~cm}, {BC}=4 {~cm}$ and ${AC}=5 {~cm}$, then ${PQ}$ (in ${cm}$ ) is equal to:

Option 1: 12

Option 2: 4.5

Option 3: 5

Option 4: 6

Team Careers360 · Accepted Answer

Correct Answer: 6

Solution :
$ riangle$ ABC ∼ $ riangle$ RPQ
$\frac{\operatorname{ar}( riangle A B C)}{\operatorname{ar}( riangle P Q R)}=\frac{4}{9}$
AB = 3 cm
BC = 4 cm
AC = 5 cm
Concept used:
$ riangle$ ABC ∼ $ riangle$ RPQ
$\frac{ ext{AB}}{ ext{RP}} = \frac{ ext{BC}}{ ext{PQ}} = \frac{ ext{AC}}{ ext{QR}} = \sqrt{\frac{ar( ext{ABC})}{ar( ext{RPQ})}}$
$\frac{ ext{AB}}{ ext{RP}} = \sqrt{\frac{4}{9}}$
Calculation:
$\frac{ ext{AB}}{ ext{RP}} = \frac{ ext{BC}}{ ext{PQ}}= \frac{2}{3}$
PQ $=\frac{3}{2} imes ext{BC}$
⇒ BC $=\frac{3}{2} imes 4 =6$
$ herefore$ The value of PQ is 6 cm.
Hence, the correct answer is 6.

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Question : Let △ABC∼△RPQ and ar(△ABC)ar(△PQR)=49. If AB=3 cm,BC=4 cm and AC=5 cm, then PQ (in cm ) is equal to:Option 1: 12Option 2: 4.5Option 3: 5Option 4: 6

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Question : Let $△ A B C \sim △ R P Q$ and $\frac{ar (△ A B C)}{ar (△ P Q R)} = \frac{4}{9}$ . If $A B = 3 c m, B C = 4 c m$ and $A C = 5 c m$ , then $P Q$ (in $c m$ ) is equal to:
Option 1: 12
Option 2: 4.5
Option 3: 5
Option 4: 6