Correct Answer: (d) 16:81
Explanation:
If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.
$\begin{array}{l}
\frac{{area\ of\ first\ triangle}}{{area\ of\ \second\ triangle}} = {\left( {\frac{{{side\ of\ first\ triangle/}}{{side\ of\ \second\ triangle}}} \right)^2}\\
= > {\left( {\frac{4}{9}} \right)^2}\\
= > \frac{{16}}{{81}}
\end{array}$
Answer
(D) is the correct option.
Note: If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. The corresponding sides of similar triangles are in proportion.
We have used the following theorem.Theorem: If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio
If two triangles are similar to each other, then the ratio of the areas of these triangles will be equal to the square of the ratio of the corresponding sides of these triangles.
It is given that the sides are in the ratio 4:9.
Therefore, ratio between areas of these triangles = `(4/9)^2 = 16/81`
Hence, the correct answer is 16 : 81.
Concept: Areas of Similar Triangles
Is there an error in this question or solution?
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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