Question

ABC~∆PQR,BC=4cm और QR=7cm, तब ABCका क्षेत्रफल: PQR का क्षेत्रफल =

(a) 4:7 (b) 16:49 (c) 44:77 (d)8:14​

Answer 1

Answer:

Given △ABC∼△DEF

In two similar triangles, the ratio of their areas is the square of the ratio of their sides

⇒

ar(DEF)

ar(ABC)

=(

EF

BC

)

2

⇒

ar(DEF)

80

=(

5

4

)

2

⇒

ar(DEF)

80

=

25

16

⇒ar(DEF)=125cm

2

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Answer 2

Given: $\[\Delta ABC \sim \Delta PQR\], BC=4 cm, QR=7cm$.

To find: the ratio of $\[ar\left( {\Delta ABC} \right):ar\left( {\Delta PQR} \right)\]$.

Solution:

Know that, In two similar triangles, the ratio of their areas is the square of the ratio of their sides.

Find the ratio of $\[ar\left( {\Delta ABC} \right):ar\left( {\Delta PQR} \right)\]$.

$\[ \Rightarrow \frac{{ar\left( {ABC} \right)}}{{ar\left( {PQR} \right)}} = {\left( {\frac{{BC}}{{QR}}} \right)^2}\]$

$\[ \Rightarrow \frac{{ar\left( {ABC} \right)}}{{ar\left( {PQR} \right)}} = {\left( {\frac{4}{7}} \right)^2}\]$

$\[ \Rightarrow \frac{{ar\left( {ABC} \right)}}{{ar\left( {PQR} \right)}} = \frac{{16}}{{49}}\]$

Therefore, the ratio of $\[ar\left( {\Delta ABC} \right):ar\left( {\Delta PQR} \right)\]$ is $16:49$.

Hence, the correct answer is option (b). i.e., $16:49$.