Two similar triangles have perimeters 30 and 50. If the triangle with smaller perimeter has area 72, what is the area of the larger triangle?

• A. 72
• B. 200
• C. 400
• D. 125

Answer: (B)

Similar shapes scale their lengths by the same factor, and their areas by the square of that factor. Perimeters also scale by the same linear factor as the sides, so the ratio of perimeters gives the scale factor.

Here, the smaller triangle has a perimeter of 30 and the larger one 50, so the linear scale factor from small to large is 50/30 = 5/3. The area scales by (5/3)^2 = 25/9. The given small-area is 72, so the large-area is 72 × 25/9 = (72/9) × 25 = 8 × 25 = 200.

Therefore, the area of the larger triangle is 200.