Question

Triangle PQR ~ Triangle XYZ and PQ/XY =5/2 then find arXYZ/arPQR

Answer 1

The value of arXYZ/arPQR is $\frac{4}{25}$.

Step-by-step explanation:

It is given that Triangle PQR ~ Triangle XYZ and PQ/XY =5/2.

We need to find the value of arXYZ/arPQR.

If two triangles are similar then ratio of their area is equal to the ratio of square of corresponding sides.

Since ΔPQR ~ ΔXYZ, so

$\dfrac{ar(XYZ)}{ar(PQR)}=\dfrac{(XY)^2}{(PQ)^2}$

$\dfrac{ar(XYZ)}{ar(PQR)}=(\dfrac{XY}{PQ})^2$

$\dfrac{ar(XYZ)}{ar(PQR)}=(\dfrac{2}{5})^2$        $[\because \dfrac{PQ}{XY}=\dfrac{5}{2}\Rightarrow \dfrac{XY}{PQ}=\dfrac{2}{5}]$

$\dfrac{ar(XYZ)}{ar(PQR)}=\dfrac{2^2}{5^2}$

$\dfrac{ar(XYZ)}{ar(PQR)}=\dfrac{4}{25}$

Therefore, the value of arXYZ/arPQR is $\frac{4}{25}$.

#Learn more

Given triangle abc is similar to pqr. If ab/pq=1/3 then Find ar abc/arpqr

https://brainly.in/question/3173320

Answer 2

Answer:

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