The ratio of the corresponding altitudes of two similar triangles is 3/5 . Is it correct to say that the ratio of their areas is 6/5? Why
Solution:
Given, the ratio of the corresponding altitudes of two similar triangles is 3/5.
We have to determine if the ratio of their areas is 6/5.
We know that,
Similar triangles have congruent corresponding angles and the corresponding sides are in proportion.
Similar triangles have the same shape, but not the same size.
By the property of similar triangles,
\((\frac{area_{1}}{area_{2}})=(\frac{altitude_{1}}{altitude_{2}})^{2}\)
LHS:area₁/area₂
= 6/5
RHS: \((\frac{altitude_{1}}{altitude_{2}})^{2}\)
= \((\frac{3}{5})^{2}\)
= 9/25
LHS ≠ RHS
The ratio of areas is not equal to the ratio of the squares of the altitude.
Therefore, the ratio of the areas is not equal to 6/5.
✦ Try This: The ratio of the corresponding altitudes of two similar triangles is 3/4 . Is it correct to say that the ratio of their areas is 9/16 ? Why
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.2 Problem 9
The ratio of the corresponding altitudes of two similar triangles is 3/5 . Is it correct to say that the ratio of their areas is 6/5? Why
Summary:
The ratio of the corresponding altitudes of two similar triangles is 3/5 . It is not correct to say that the ratio of their areas is 6/5 since it does not satisfy the property of similar triangles
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