Two triangles are similar with sides in the ratio 3:5. What is the ratio of their areas?

Question

Two triangles are similar with sides in the ratio 3:5. What is the ratio of their areas?

1. A. 3:5
2. B. 5:3
3. C. 9:25 (Correct answer)
4. D. 25:9

Correct Answer

Option C — 9:25

Detailed Solution & Explanation

The correct answer is 9:25.

Key Points

• In similar figures the ratio of areas is the square of the ratio of corresponding sides.
• Sides in $3 : 5$ therefore give areas in $3^2 : 5^2 = $ 9 : 25.

Additional Information

• The companion results: perimeters scale like the sides (3 : 5), and volumes of similar solids scale like the cube (27 : 125).
• This follows because area has two dimensions of length — scaling each by 3/5 multiplies the area by $(3/5)^2$.
• 25 : 9 is the reversal trap; keep the order in which the triangles were named.

प्रश्न (हिन्दी में)

दो त्रिभुज समरूप हैं जिनकी भुजाओं का अनुपात 3:5 है। उनके क्षेत्रफलों का अनुपात क्या है?

1. A. 3:5
2. B. 5:3
3. C. 9:25
4. D. 25:9