Quant Exam > Quant Questions > The area of similar triangles, ABC and DEF ar...
Start Learning for Free
The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger △ABC be 36 cm, then the longest side of the smaller △DEF is:
- a)27 cm
- b)26 cm
- c)29 cm
- d)30 cm
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respe...
Most Upvoted Answer
The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respe...
What we need to know here is,
Supplement angles means. Sum of both the angle is 180
X+5X =180
Thay means,
X=30
Other angle is 150
Supplement angles means. Sum of both the angle is 180
X+5X =180
Thay means,
X=30
Other angle is 150
Free Test
FREE
| Start Free Test |
Community Answer
The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respe...
Given:
- The area of triangle ABC is 144 cm^2.
- The area of triangle DEF is 81 cm^2.
- The longest side of triangle ABC is 36 cm.
To find:
- The length of the longest side of triangle DEF.
Explanation:
Step 1: Finding the Scale Factor
- The area of a triangle is given by the formula: Area = (1/2) * base * height.
- Since the triangles ABC and DEF are similar, their areas are proportional to the square of their corresponding sides.
- Therefore, we can write: (AB/DE)^2 = Area of ABC/Area of DEF.
- Substituting the given values, we get: (AB/DE)^2 = 144/81.
- Simplifying the equation, we have: (AB/DE)^2 = 16/9.
- Taking the square root of both sides, we get: AB/DE = √(16/9).
- Simplifying further, we have: AB/DE = 4/3.
- This ratio represents the scale factor between the two triangles.
Step 2: Finding the Length of the Longest Side of Triangle DEF
- The longest side of triangle ABC is given as 36 cm.
- Using the scale factor, we can write: AB/DE = 4/3.
- Substituting the values, we have: 36/DE = 4/3.
- Cross-multiplying, we get: 4DE = 36 * 3.
- Simplifying the equation, we have: 4DE = 108.
- Dividing both sides by 4, we get: DE = 27.
- Therefore, the length of the longest side of triangle DEF is 27 cm.
Conclusion:
- The length of the longest side of triangle DEF is 27 cm.
- Hence, the correct answer is option A.
- The area of triangle ABC is 144 cm^2.
- The area of triangle DEF is 81 cm^2.
- The longest side of triangle ABC is 36 cm.
To find:
- The length of the longest side of triangle DEF.
Explanation:
Step 1: Finding the Scale Factor
- The area of a triangle is given by the formula: Area = (1/2) * base * height.
- Since the triangles ABC and DEF are similar, their areas are proportional to the square of their corresponding sides.
- Therefore, we can write: (AB/DE)^2 = Area of ABC/Area of DEF.
- Substituting the given values, we get: (AB/DE)^2 = 144/81.
- Simplifying the equation, we have: (AB/DE)^2 = 16/9.
- Taking the square root of both sides, we get: AB/DE = √(16/9).
- Simplifying further, we have: AB/DE = 4/3.
- This ratio represents the scale factor between the two triangles.
Step 2: Finding the Length of the Longest Side of Triangle DEF
- The longest side of triangle ABC is given as 36 cm.
- Using the scale factor, we can write: AB/DE = 4/3.
- Substituting the values, we have: 36/DE = 4/3.
- Cross-multiplying, we get: 4DE = 36 * 3.
- Simplifying the equation, we have: 4DE = 108.
- Dividing both sides by 4, we get: DE = 27.
- Therefore, the length of the longest side of triangle DEF is 27 cm.
Conclusion:
- The length of the longest side of triangle DEF is 27 cm.
- Hence, the correct answer is option A.
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer?
Question Description
The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer?.
The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer?.
Solutions for The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup