If the ratio of perimeters of two similar triangles is 9 : 16, then the ratio of their altitudes is

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Solution:

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides

Given that,

Sides of two similar triangles are in the ratio 4: 9.

We know that,

The ratio of the areas of two similar triangles = square of the ratio of their corresponding sides

= (4: 9)2

= 16 : 81

Thus option (D) 16: 81 is the correct answer.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 6

Video Solution:

Sides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the ratio (A) 2 : 3 (B) 4: 9 (C) 81: 16 (D) 16: 81

NCERT Class 10 Maths Solutions Chapter 6 Exercise 6.4 Question 9

Summary:

The sides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the ratio 16: 81.

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In a ΔPQR, S and T are the points on PQ and PR respectively, such that ST || QR and

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