Final answer:
To calculate the area of the larger triangle in similar triangles with the side ratio 2:3, we square the scale factor to find the ratio of the areas as 4:9. With the smaller triangle's area as 48 cm², we determine through a proportion that the area of the larger triangle is 108 cm².
Step-by-step explanation:
The question involves finding the area of the larger triangle when the sides of two similar triangles are in a ratio of 2:3 and the area of the smaller triangle is given. The ratio of areas of similar figures is the square of the scale factor. Since the ratio of the sides is 2:3, the scale factor is 2 for the smaller triangle and 3 for the larger triangle.
To find the ratio of their areas, we square the scale factors. So, the ratio of the areas is 22:32, or 4:9. Now, we can compare the areas using this ratio. If the smaller triangle has an area of 48 cm2, we can set up a proportion to find the area of the larger triangle:
4:9 = 48:x, where x is the area of the larger triangle. By cross multiplying, we get 4x = 432, and solving for x gives us x = 108 cm2.
Therefore, the area of the larger triangle is 108 cm2.