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The perimeters of two similar triangles ΔABC and ΔPQR are 36 cm and 24 cm respectively. If PQ = 10 cm, the AB is (SSC CHSL 2014)
- a)15 cm
- b)12 cm
- c)14 cm
- d)26 cm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The perimeters of two similar triangles ΔABC and ΔPQR are ...
ΔABC ~ ΔPQR (given)
(Corresponding sides are proportional)
(Corresponding sides are proportional)
Most Upvoted Answer
The perimeters of two similar triangles ΔABC and ΔPQR are ...
Understanding Similar Triangles
Similar triangles have proportional sides and equal corresponding angles. The ratio of their perimeters is equal to the ratio of the lengths of their corresponding sides.
Given Data
- Perimeter of triangle ΔABC = 36 cm
- Perimeter of triangle ΔPQR = 24 cm
- Length of side PQ = 10 cm
Finding the Ratio of Similarity
- The ratio of the perimeters of ΔABC to ΔPQR is:
Perimeter Ratio = (Perimeter of ΔABC) / (Perimeter of ΔPQR) = 36 cm / 24 cm = 3 / 2
Calculating the Length of AB
- Since the triangles are similar, the lengths of their corresponding sides are in the same ratio. Thus, we can express the relationship as:
AB / PQ = Perimeter Ratio
AB / 10 cm = 3 / 2
- To find AB, cross-multiply:
AB = PQ × (Perimeter Ratio)
AB = 10 cm × (3 / 2)
AB = 10 cm × 1.5 = 15 cm
Conclusion
The length of side AB in triangle ΔABC is 15 cm. Thus, the correct answer is option A.
Similar triangles have proportional sides and equal corresponding angles. The ratio of their perimeters is equal to the ratio of the lengths of their corresponding sides.
Given Data
- Perimeter of triangle ΔABC = 36 cm
- Perimeter of triangle ΔPQR = 24 cm
- Length of side PQ = 10 cm
Finding the Ratio of Similarity
- The ratio of the perimeters of ΔABC to ΔPQR is:
Perimeter Ratio = (Perimeter of ΔABC) / (Perimeter of ΔPQR) = 36 cm / 24 cm = 3 / 2
Calculating the Length of AB
- Since the triangles are similar, the lengths of their corresponding sides are in the same ratio. Thus, we can express the relationship as:
AB / PQ = Perimeter Ratio
AB / 10 cm = 3 / 2
- To find AB, cross-multiply:
AB = PQ × (Perimeter Ratio)
AB = 10 cm × (3 / 2)
AB = 10 cm × 1.5 = 15 cm
Conclusion
The length of side AB in triangle ΔABC is 15 cm. Thus, the correct answer is option A.
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Community Answer
The perimeters of two similar triangles ΔABC and ΔPQR are ...
ΔABC ~ ΔPQR (given)
(Corresponding sides are proportional)
(Corresponding sides are proportional)
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The perimeters of two similar triangles ΔABC and ΔPQR are 36 cm and 24 cm respectively. If PQ = 10 cm, the AB is (SSC CHSL 2014)a)15 cmb)12 cmc)14 cmd)26 cmCorrect answer is option 'A'. Can you explain this answer?
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The perimeters of two similar triangles ΔABC and ΔPQR are 36 cm and 24 cm respectively. If PQ = 10 cm, the AB is (SSC CHSL 2014)a)15 cmb)12 cmc)14 cmd)26 cmCorrect answer is option 'A'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about The perimeters of two similar triangles ΔABC and ΔPQR are 36 cm and 24 cm respectively. If PQ = 10 cm, the AB is (SSC CHSL 2014)a)15 cmb)12 cmc)14 cmd)26 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeters of two similar triangles ΔABC and ΔPQR are 36 cm and 24 cm respectively. If PQ = 10 cm, the AB is (SSC CHSL 2014)a)15 cmb)12 cmc)14 cmd)26 cmCorrect answer is option 'A'. Can you explain this answer?.
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