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What is the area of the triangle formed between the lines y – x =2, 3x + 4y = 29 and y = 2?
- a)4.5
- b)6
- c)9
- d)10.5
- e)12
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the area of the triangle formed between the lines y – x ...
Given
3 lines:
- y – x = 2
- 3x + 4y = 29
- y = 2
To Find : The area of the triangle formed between these 3 lines
Approach:
- In order to find the area, we first need to know the coordinates of the 3 vertices of the triangle formed.
- Each vertex of the triangle is the point of intersection of 2 of these 3 given lines. So, we’ll solve each pair of 2 lines to determine their point of intersection (that is, the vertices of the triangle)
- Then, we’ll plot these plots in the x-y plane and find the area of the triangle.
Working out:
Finding the vertices of the triangle
- Let’s find these vertices one by one:
- Intersection of y-x =2 and 3x +4y =29
- From y – x = 2, we get y = x + 2
- Substituting this in the equation 3x + 4y = 29, we get:
- 3x + 4(x+2) = 29
- 7x + 8 = 29
- 7x = 21
- So, x = 3
- And, y = 3+2 = 5
- So, one vertex of the triangle is (3,5)
- Intersection of y-x =2 and y=2
- Putting y = 2 in y – x = 2, we get 2 – x = 2. So, x = 0
- So, the 2 vertex of the triangle is (0,2)
- Intersection of 3x +4y =29 and y=2
- Putting y = 2 in 3x + 4y = 29, we get 3x + 4(2) = 29
- 3x = 21
- So, x = 7
- The y-coordinate of this vertex will of course be 2 only
- So, the 3 vertex of the triangle is (7,2)
- So, we can represent the triangle as under:
Finding the area of the triangle
Looking at the answer choices, we see that the correct answer is Option D
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What is the area of the triangle formed between the lines y – x =2, 3x + 4y = 29 and y = 2?a)4.5b)6c)9d)10.5e)12Correct answer is option 'D'. Can you explain this answer?
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What is the area of the triangle formed between the lines y – x =2, 3x + 4y = 29 and y = 2?a)4.5b)6c)9d)10.5e)12Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the area of the triangle formed between the lines y – x =2, 3x + 4y = 29 and y = 2?a)4.5b)6c)9d)10.5e)12Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the area of the triangle formed between the lines y – x =2, 3x + 4y = 29 and y = 2?a)4.5b)6c)9d)10.5e)12Correct answer is option 'D'. Can you explain this answer?.
What is the area of the triangle formed between the lines y – x =2, 3x + 4y = 29 and y = 2?a)4.5b)6c)9d)10.5e)12Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the area of the triangle formed between the lines y – x =2, 3x + 4y = 29 and y = 2?a)4.5b)6c)9d)10.5e)12Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the area of the triangle formed between the lines y – x =2, 3x + 4y = 29 and y = 2?a)4.5b)6c)9d)10.5e)12Correct answer is option 'D'. Can you explain this answer?.
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