Above are two different models of the same triangle. If the area of the model on the right is 9 sq in, what is the area of the model on the left?
Since both models are of the same triangle, they are similar and proportional.
Let the area of the model on the left be x sq in.
Therefore, the ratio of the areas of the two models is 9/x.
Since the models are similar triangles, the ratio of their sides is the same as the ratio of their areas.
Let the sides of the triangle in the left model be a and the corresponding side in the right model be b.
We can write the ratio of sides as a/b = x/9.
Since the models are similar triangles, the ratio of their sides is equal to the ratio of their areas, we have:
(x/9)^2 = 9/x
Multiplying both sides by 81x:
x^3 = 81^2
x = 81
Therefore, the area of the model on the left is 81 sq in.