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Question

The areas of two similar triangles are 100 cm2 and 64 cm2 respectively. If the median of greater side of the first triangle is 13 cm, find the corresponding median of the other triangle.

A
20 cm
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B
15 cm
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C
10 cm
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D
10.4 cm
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Solution

The correct option is D 10.4 cm
Given that the areas of two similar triangles are 100 cm2 and 64 cm2.
and median of greater triangle is 13 cm.
Let the median of the other triangle be x cm

We know that, the areas of two similar triangles are in the ratio of the squares of their corresponding sides or medians.

The ratio of the areas of triangles =10064=2516

(13)2(x)2=2516

169x2=2516

25x2=169×16

x2=270425=108.16

x=10.4 cm

Hence, the median of the other triangle is 10.4 cm

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