Tag: properties of parallel lines and their transversal

Questions Related to properties of parallel lines and their transversal

Ratio of two corresponding sides of two similar triangles is $4:9$. Then ratio of their area is ___.

maths properties of parallel lines and their transversal introduction to shapes similarity of triangles introduction to similar triangles

  1. $\dfrac{16} {81}$

  2. $\dfrac{34} {81}$

  3. $\dfrac{81} {16}$

  4. $None\ of\ these$

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Correct Option: A
Explanation:

Ratio of areas of two similar triangles is equal to the squares of the ratio of their sides.

Ratio of sides $=\dfrac{4}{9}$
Ratio of areas $=\left( \dfrac { 4 }{ 9 }  \right) ^{ 2 }=\dfrac { 16 }{ 81 } $

$\triangle PQR \sim \triangle XYZ, \dfrac{XY}{PQ}=\dfrac{3}{2}$ then $\dfrac{Area\ of\ \triangle PQR}{Area\ of\ \triangle XYZ}=$____.

maths properties of parallel lines and their transversal introduction to shapes similarity of triangles introduction to similar triangles

  1. $\dfrac{9}{4}$

  2. $\dfrac{4}{9}$

  3. $\dfrac{3}{2}$

  4. $\dfrac{2}{3}$

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Correct Option: B
Explanation:

$\dfrac{{XY}}{{PQ}} = \dfrac{3}{2}$


$ \Rightarrow \dfrac{{PQ}}{{XY}} = \dfrac{2}{3}$


Now,  $\dfrac{{Area{\rm{ of  }}\Delta {\rm{PQR}}}}{{Area{\rm{ of  }}\Delta {\rm{XYZ}}}} = {\left( {\dfrac{2}{3}} \right)^2} = \dfrac{4}{9}$