Question

find the perimeter of the large triangle. options: 54, 12, 24, 36

Explanation:

Step1: Identify Similar Triangles

The two triangles are similar (right triangles, corresponding sides proportional: $\frac{3}{9}=\frac{4}{12}=\frac{5}{15}=\frac{1}{3}$? Wait, no, $\frac{3}{9}=\frac{1}{3}$, $\frac{4}{12}=\frac{1}{3}$, $\frac{5}{15}=\frac{1}{3}$. Wait, the small triangle has legs 3, 4, hypotenuse 5. The large triangle has leg 9 (3×3), leg 12 (4×3), hypotenuse 15 (5×3). Wait, but in the image, small triangle: 3,4,5; large triangle: 9,12,15? Wait, the large triangle's legs: one is 9 (base), the other is 12 (height), hypotenuse 15. Wait, perimeter of small triangle: 3+4+5=12. Scale factor: large/small = 3 (since 9/3=3, 12/4=3, 15/5=3). So perimeter of large triangle: 12×3=36? Wait, but the options have 36 as option 4. Wait, let's check again. Small triangle sides: 3,4,5 (perimeter 12). Large triangle sides: 9 (3×3), 12 (4×3), 15 (5×3). Perimeter: 9+12+15=36.

Step2: Calculate Perimeter

Perimeter of large triangle = 9 + 12 + 15 = 36.

Answer:

36 (or the option with 36, e.g., 4. 36)