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Geometry
Similar Triangles
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RRB NTPC Graduate Tier 1 2025 Shift-3 📅 06 Jun, 2025

If $\triangle ABC \sim \triangle XYZ$, $AB=6$ cm, $XY=8$ cm, $YZ=12$ cm and $ZX=16$ cm, then find the perimeter of $\triangle ABC$.

A
34 cm
B
32 cm
C
27 cm
D
24 cm
Result Summary
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RRB NTPC Graduate Tier 1
2025 • 06 Jun, 2025 • Shift-3
If $\triangle ABC \sim \triangle XYZ$, $AB=6$ cm, $XY=8$ cm, $YZ=12$ cm and $ZX=16$ cm, then find the perimeter of $\triangle ABC$.
Correct Answer
27 cm
Property of Similar Triangles: When two triangles are similar ($\triangle ABC \sim \triangle XYZ$), the ratio of their perimeters is strictly equal to the ratio......
Ref/Book : RRB NTPC Graduate Tier 1 2025
Ref. Subject Geometry
Chapter -
Ref. Topic Similar Triangles
Pg. No -
💡 Analysis & Explanation
Property of Similar Triangles ▼
When two triangles are similar ($\triangle ABC \sim \triangle XYZ$), the ratio of their perimeters is strictly equal to the ratio of their corresponding sides.
Calculating Perimeter of $\triangle XYZ$ ▼
The perimeter of $\triangle XYZ$ is the sum of its sides: $XY + YZ + ZX = 8 + 12 + 16 = 36$ cm.
Establishing the Ratio ▼
The ratio of corresponding sides $AB/XY = 6/8 = 3/4$. Therefore, the ratio of their perimeters is also 3/4. So, Perimeter of $\triangle ABC$ / Perimeter of $\triangle XYZ$ = 3/4.
Final Calculation ▼
Perimeter of $\triangle ABC$ / 36 = 3/4. Multiplying both sides by 36 gives Perimeter of $\triangle ABC$ = $3/4 \times 36 = 3 \times 9 = 27$ cm.
Conclusion ▼
The perimeter of $\triangle ABC$ is exactly 27 cm.
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