Sides of two similar triangles are in the ratio of 4:9. Area of these triangles are in the ratio of …………
Sides of two similar triangles are in the ratio of 4:9. Area of these triangles are in the ratio of …………
A) 2 : 3
B) 4 : 9
C) 81 : 16
D) 16 : 81
4 views
2 Answers
Correct option is (D) 16 : 81
Given that sides of two similar triangles are in the ratio of 4:9.
i.e., \(\frac{S_1}{S_2}=\frac49\)
We know that the ratio of areas of two similar triangle is square of the ratio of sides of both similar triangles.
i.e., \(\frac{A_1}{A_2}=(\frac{S_1}{S_2})^2\)
\(=(\frac49)^2=\frac{16}{81}\)
Hence, area of these two similar triangles are in the ratio of 16:81.
4 views
Answered