The triangle ABC is similar to the triangle DEF.
The ratio between the lengths of their sides is 9:8.
What is the ratio between the areas of the triangles?
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The triangle ABC is similar to the triangle DEF.
The ratio between the lengths of their sides is 9:8.
What is the ratio between the areas of the triangles?
We multiply the ratio by 2
Raised to the power of 2:
81:64
If it is known that both triangles are equilateral, are they therefore similar?
Because area is a 2D measurement! When you scale a triangle by factor 9:8, both length AND width scale by that ratio, so area scales by .
Perimeter ratio would be the same as the side ratio (9:8) because perimeter is a 1D measurement. Only areas and volumes get squared or cubed!
Think dimensions: 1D measurements (length, perimeter) keep the original ratio. 2D measurements (area) square it. 3D measurements (volume) cube it.
Yes! as a decimal. Both forms are correct, but ratios like 81:64 often show the relationship more clearly in geometry problems.
That's not how ratios work! 18:16 simplifies to 9:8, which is the side ratio, not the area ratio. You need to square each number: .
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