Question

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

Answer 1

Answer:

The ratio of the areas of two triangles is 16 : 81.

Among the given options option (d) 16 : 81 is the correct answer.

Step-by-step explanation:

Given:

The corresponding sides of two similar triangles are in the ratio 4 : 9

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of any two corresponding sides.

ar(∆1/)ar(∆2) = (side1/ side 2)²

ar(∆1)/ar(∆2) = (4/9)²

ar(∆1)/ar(∆2) = 16/81

ar(∆1)/ar(∆2) = 16/81

ar(∆1)/ar(∆2) = 16 : 81

Hence, the ratio of the areas of two triangles is 16 : 81.

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