If in two similar triangles, the ratio of their corresponding sides is 4:9, then the ratio of their areas is:
Similar triangles are triangles that have the same shape but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional. This means one triangle can be obtained by enlarging or shrinking the other. Similar triangles are important in geometry and help solve problems involving scale maps and architectural designs.
Class 10 Maths Chapter 6 Triangles is a crucial part of the CBSE Exam 2024-25 syllabus. It covers topics like similarity criteria theorems and Pythagoras theorem. Understanding these concepts is essential for solving problems related to congruence and proportions. This chapter strengthens logical reasoning and geometric skills which are vital for higher studies and practical applications in fields like architecture and engineering.
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In two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Given that the ratio of the corresponding sides is 4:9, the ratio of their areas can be calculated as:
(Ratio of areas ) = ( Ratio of sides )²
= ( 4:9 )²
= 4² : 9²
= 16:81
Thus, the correct answer is 16:81.
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