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The ratio of the sides of two similar triangles is 4 : 5. The ratio of the areas of these two triangles is:
2 : 2.5
8 : 10
16 : 25
4 : 5
16 : 25
Whenever two triangles are similar, simply square the terms of the given side ratio to get the area ratio directly (e.g., 42:52).
The ratio of the corresponding sides of two similar triangles is 4 : 5.
Area2тАЛArea1тАЛтАЛ=(Side2тАЛSide1тАЛтАЛ)2
Whenever two triangles are similar, simply square the terms of the given side ratio to get the area ratio directly (e.g., 42:52).
Students often make the mistake of assuming the area ratio is the same as the side ratio or that the perimeter ratio is the same as the area ratio.
Identify the Property of Similar Triangles
For any two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Area(╬Ф2тАЛ)Area(╬Ф1тАЛ)тАЛ=(S2тАЛS1тАЛтАЛ)2
Substitute the Given Values
Given the side ratio is 4:5, we substitute S1тАЛ=4 and S2тАЛ=5 into the formula.
Area(╬Ф2тАЛ)Area(╬Ф1тАЛ)тАЛ=(54тАЛ)2
Calculate the Result
Squaring both the numerator and the denominator, we get 42=16 and 52=25.
2516тАЛ
C is correct because the ratio of the areas of two similar triangles is the square of the ratio of their sides, which results in 16:25.
This concept is specific to Area. For Perimeters or altitudes of similar triangles, the ratio remains the same as the sides, 4:5, not squared.
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