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Two triangles ABC and PQR are similar to each other in which AB = 10 cm, PQ = 8 cm. Then the ratio of the areas of triangles ABC and PQR is :
1. 4 : 5
2. 25 : 16
3. 64 : 125
4. 4 : 7

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Correct Answer - Option 2 : 25 : 16

Given

Two triangles ABC and PQR are similar to each other in which AB = 10 cm, PQ = 8 cm.

Concept used

Similarity of trianlges

Calculation

Ratio of areas of two triangles = Ratio of squares of corresponding sides of triangles

\(\frac{{Area\ of\ \Delta ABC}}{{Area\ of\ \Delta PQR}} = \frac{{{{\left( {AB} \right)}^2}}}{{{{\left( {PQ} \right)}^2}}}\)

\(\frac{{Area\ of\ \Delta ABC}}{{Area\ of\ \Delta PQR}} = \frac{{{{\left( {10} \right)}^2}}}{{{{\left( {8} \right)}^2}}}\)

\(\frac{{Area\ of\ \Delta ABC}}{{Area\ of\ \Delta PQR}} = \frac{{100}}{{64}}\)

\(\frac{{Area\ of\ \Delta ABC}}{{Area\ of\ \Delta PQR}} = \frac{{25}}{{16}}\)

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