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The perimeters of Δ ABC and Δ DEF are 36 cm and 54 cm respectively. AB = 12 cm. If both are similar triangles, find side DE.
- a)20
- b)16
- c)24
- d)18
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The perimeters of Δ ABC and Δ DEF are 36 cm and 54 cm respectively. A...
Given:
Perimeters of Δ ABC and Δ DEF are 36 cm and 54 cm respectively
Both triangles are similar.
Concept used:If two triangles are similar then the ratio of the corresponding sides is equal to the ratio of perimeter of the triangle.
Calculation:
Here, ΔABC ~ Δ DEF
If two triangles are similar then the ratio of the corresponding sides is equal to the ratio of perimeter of the triangle
Perimeter of ΔABC/Perimeter of ΔDEF = AB/DE = BC/EF = AC/DF
Perimeter of ΔABC/Perimeter of ΔDEF = AB/DE
⇒ 36/54 = 12/DE
⇒ DE = (54 × 12)/36
⇒ DE = 18 cm
∴ The value DE is 18 cm.
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The perimeters of Δ ABC and Δ DEF are 36 cm and 54 cm respectively. A...
Given information:
- The perimeter of triangle ABC is 36 cm.
- The perimeter of triangle DEF is 54 cm.
- AB = 12 cm.
To find: Side DE.
To solve this problem, we can use the concept of similarity of triangles.
1. Understanding similarity of triangles:
- Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are in proportion.
- If two triangles are similar, the ratio of their corresponding sides will be equal.
2. Finding the ratio of perimeters:
- The ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides.
- Let's assume the ratio of the perimeters of triangle ABC and triangle DEF is x.
- Therefore, we can write the equation:
Perimeter of ABC / Perimeter of DEF = x
36 / 54 = x
Simplifying, we get:
2 / 3 = x
3. Finding the ratio of sides:
- Since triangle ABC and triangle DEF are similar triangles, the ratio of their corresponding sides will be equal to x.
- Let's assume the ratio of side AB and side DE is also x.
- Therefore, we can write the equation:
AB / DE = x
12 / DE = 2 / 3
Cross-multiplying, we get:
3 * 12 = 2 * DE
36 = 2 * DE
Simplifying, we get:
DE = 18 cm
Therefore, the length of side DE is 18 cm.
Hence, the correct answer is option 'D'.
- The perimeter of triangle ABC is 36 cm.
- The perimeter of triangle DEF is 54 cm.
- AB = 12 cm.
To find: Side DE.
To solve this problem, we can use the concept of similarity of triangles.
1. Understanding similarity of triangles:
- Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are in proportion.
- If two triangles are similar, the ratio of their corresponding sides will be equal.
2. Finding the ratio of perimeters:
- The ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides.
- Let's assume the ratio of the perimeters of triangle ABC and triangle DEF is x.
- Therefore, we can write the equation:
Perimeter of ABC / Perimeter of DEF = x
36 / 54 = x
Simplifying, we get:
2 / 3 = x
3. Finding the ratio of sides:
- Since triangle ABC and triangle DEF are similar triangles, the ratio of their corresponding sides will be equal to x.
- Let's assume the ratio of side AB and side DE is also x.
- Therefore, we can write the equation:
AB / DE = x
12 / DE = 2 / 3
Cross-multiplying, we get:
3 * 12 = 2 * DE
36 = 2 * DE
Simplifying, we get:
DE = 18 cm
Therefore, the length of side DE is 18 cm.
Hence, the correct answer is option 'D'.
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The perimeters of Δ ABC and Δ DEF are 36 cm and 54 cm respectively. AB = 12 cm. If both are similar triangles, find side DE.a)20b)16c)24d)18Correct answer is option 'D'. Can you explain this answer?
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