If two similar triangles have perimeters in ratio 3:5 and the smaller triangle has area 72, what is the larger's area?

• A. 400
• B. 200
• C. 125
• D. 72

Answer: (B)

When two triangles are similar, all linear dimensions scale by the same factor as the perimeters, and areas scale by the square of that factor. The given perimeter ratio 3:5 means the linear scale from the smaller to the larger triangle is 5/3. Therefore, the area scales by (5/3)² = 25/9.

So the larger area is 72 × 25/9 = (72/9) × 25 = 8 × 25 = 200.