- A9 : 25
- B3 : 5
- C5 : 3
- D6 : 10
Step-by-Step Solution
In similar triangles the ratio of perimeters equals the ratio of corresponding sides, so it is 3 : 5.
Answer: B) 3 : 5
Two similar triangles have corresponding sides in ratio 3 : 5. The ratio of their perimeters is ____.
Class 10Triangles (Similarity)Geometry — Similarity
Key idea: Areas of similar triangles
**Theorem**: The ratio of the areas of two similar triangles is equal to the SQUARE of the ratio of their corresponding sides.
If ΔABC ~ ΔDEF with scale factor , then
Area(ABC)/Area(DEF) = .
**Why**: area scales as length × length. If both length and breadth scale by , area scales by .
**Example**: Two similar triangles have corresponding sides in ratio 3:5. Area ratio = 9:25.
**Reverse**: if areas are in ratio 16:25, sides are in ratio 4:5 (square root).
If ΔABC ~ ΔDEF with scale factor , then
Area(ABC)/Area(DEF) = .
**Why**: area scales as length × length. If both length and breadth scale by , area scales by .
**Example**: Two similar triangles have corresponding sides in ratio 3:5. Area ratio = 9:25.
**Reverse**: if areas are in ratio 16:25, sides are in ratio 4:5 (square root).
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More Class 10 Triangles (Similarity) practice
In ΔABC, DE ∥ BC with D on AB and E on AC. If AD = 2 cm, DB = 3 cm and AC = 10 cm, find…ΔABC ~ ΔDEF with a scale factor (AB : DE) of 3 : 4. If the area of ΔABC is 45 cm², find…The square of the hypotenuse of a right triangle equals the sum of the squares of the…A right triangle has legs 3 cm and 4 cm. Find the length of its hypotenuse in cm.If ΔABC ~ ΔPQR, then which of the following is NOT necessarily true?