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The ratio of the lengths of two corresponding sides of two similar triangles is 6 : 2. The ratio of the areas of these two triangles, in the order mentioned, is:
1
36:4 or 9:1
6 : 2
12:4
6 : 2
Whenever given the ratio of sides of similar triangles, simply square each term of the ratio to get the ratio of their areas.
The ratio of the lengths of corresponding sides of two similar triangles is 6 : 2.
Area2тАЛArea1тАЛтАЛ=(side2тАЛside1тАЛтАЛ)2
Whenever given the ratio of sides of similar triangles, simply square each term of the ratio to get the ratio of their areas.
Students often mistakenly divide the side ratio by 2 or square only one side, forgetting that the property applies to the square of the ratio of corresponding linear dimensions.
Identify the Property
For any two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Area2тАЛArea1тАЛтАЛ=(side2тАЛside1тАЛтАЛ)2
Apply Given Values
Given the ratio of sides is 6:2, we substitute these values into the formula.
Area2тАЛArea1тАЛтАЛ=(26тАЛ)2
Calculate the Square
Calculating the square of the ratio gives (6)2:(2)2.
62:22=36:4
C is correct because the ratio of areas of similar triangles is the square of the ratio of their corresponding sides, which results in 36:4.
This property also applies to 3D similar shapes (like spheres or cubes), where the ratio of volumes is the cube of the ratio of corresponding linear dimensions (e.g., side3).
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