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The areas of two similar triangles are 81 sq cm and 49 sq cm respectively. If the altitude of the first triangle is 6.3 cm, then the corresponding altitude of the other is,

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4.9cm

4cm

3.5cm

4.2cm

answer is A.

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Detailed Solution

Given that,
The areas of two similar triangles are 81 sq cm and 49 sq cm respectively.
According to the question,
The area of the first triangle is

A 1 = 81 c m 2 .

The area if the second similar triangle is

A 2 = 49 c m 2

The altitude of first triangle is

x = 6.3

cm
The ratio of the areas of two similar triangles equals the ratio of the square of the corresponding altitudes of the triangles.
Then, if y is the altitude of the second triangle,

A 1 A 2 = x 2 y 2 ⇒ 8149 = 6.3 2 y 2 ⇒ 8149 = 6.3 y

⇒ 97 = 6.3 y ⇒ y = 6.3 7 9 ⇒ y = 0.7 7

⇒ y = 4.9

cm
The corresponding altitude of the other similar triangle is 4.9 cm.
Hence, option 1 is correct.

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