Question

If the ratio of area of two similar triangles is 64:81 then the ratio of their sides is
A)8:9

B)9:8

D)3:4

C)4:3

Answer 1

ACCORDING TO ME , 8:9 IS THE CORRECT ANSWER .

EXPLANATION - 64:81 = 64/81 = √64/√81

= 8/9

RATIO COMES OUT TO BE 8 : 9

(Concept used = The Area of triangle is equal to the square of its corresponding sides . )

Answer 2

The ratio of the sides of the two similar triangles is (A) 8: 9.

Given: The ratio of the area of two similar triangles is 64: 81.

To Find: The ratio of the sides of the two similar triangles.

Solution:

• When two triangles are said to be similar, then the ratio of the areas of the two triangles is said to be in equal proportion.
• When two triangles are said to be similar, then the ratio of the sides of the two triangles is said to be in equal proportion.
• We can say that the relation between the area and length of the sides of the two triangles can be given by,

                     A1 / A2 = ( S1 / S2 )²                                                    .....(1)

Where A1 = Area of the first triangle, S1 = Side length of the first triangle, A2 = Area of the second triangle, and S2 = Side length of the second triangle.

Coming to the numerical, we are given;

The ratio of the  area of two similar triangles is = 64: 81

So, we can say that;

               A1 / A2 = 64 / 81

Let the side lengths of the first and second triangle be S1 and S2 respectively.

So, from (1), we can say that,

              A1 / A2 = ( S1 / S2 )²  

         ⇒ ( S1 / S2 )² = 64 / 81

         ⇒ ( S1 / S2 ) = √( 64 / 81 )

         ⇒  S1 / S2 = 8 / 9

Hence, the ratio of the sides of the two similar triangles is (A) 8: 9.

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