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Home » The areas of two similar triangles are 64cm2 and 100cm2 respectively. If a median of the smaller triangle is 5.6cm, find the corresponding median of the other.
The areas of two similar triangles are 64cm2 and 100cm2 respectively. If a median of the smaller triangle is 5.6cm, find the corresponding median of the other.
CBSE | Class 10 | Exercise 4C | Maths | RS Aggarwal | Triangles
The areas of two similar triangles are 64cm2 and 100cm2 respectively. If a median of the smaller triangle is 5.6cm, find the corresponding median of the other.

 

 

 

Answer:

Let the two triangles be ABC and PQR with medians AM and PN,

The ratio of areas of two similar triangles will be equal to the ratio of squares of their corresponding medians.

\frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\Delta P Q R)}=\frac{A M^{2}}{P N^{2}}

\frac{64}{100}=\frac{5.6^{2}}{P N^{2}}

P N^{2}=\frac{64}{100} \times 5.6^{2}

P N^{2}=\sqrt{\frac{64}{100} \times 5.6 \times 5.6}

\therefore P N=7 \mathrm{~cm}

The median of the larger triangle is 7 cm.

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