If the ratio of the perimeters of two triangles is , and the area of the larger triangle is , what is the area of the smaller
triangle?
Select one:
a.
b.
c.
d.

To find the area of the smaller triangle given that the ratio of the perimeters is , we can use the fact that the ratio of the areas of two similar triangles is the square of the ratio of their corresponding lengths, which in this case is the ratio of the perimeters.

The area ratio would then be:

If the area of the larger triangle is , we can set up the proportion:

Cross-multiplying gives us:

Calculating :

Now, we solve for :

Thus, the area of the smaller triangle is , which corresponds to option a.

a.