SSC CGL Exam > SSC CGL Questions > The area of the triangle formed by the line 5...
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The area of the triangle formed by the line 5x + 7y = 35, 4x + 3y = 12 and x-axis is
- a)160/13 sq.unit
- b)150/13 q.untit
- c)140/13 sq.unit
- d)10 sq. unit
Correct answer is option 'A'. Can you explain this answer?
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The area of the triangle formed by the line 5x + 7y = 35, 4x + 3y = 12...
To find the area of the triangle formed by the lines 5x - 7y = 35, 4x - 3y = 12, and the x-axis, we can use the concept of determinants.
We have two equations:
1. 5x - 7y = 35
2. 4x - 3y = 12
First, let's find the intersection points of these two lines.
Solving these equations simultaneously, we get:
1. 5x - 7y = 35 => y = (5x - 35)/7 => y = (5/7)x - 5
2. 4x - 3y = 12 => y = (4x - 12)/3 => y = (4/3)x - 4
Setting y = 0 in both equations, we can find the x-intercepts of the lines:
1. (5/7)x - 5 = 0 => (5/7)x = 5 => x = 7
2. (4/3)x - 4 = 0 => (4/3)x = 4 => x = 3
So the intersection points are (7, 0) and (3, 0).
Now, let's find the equation of the third line, which is the x-axis. The equation of the x-axis is y = 0.
We can now calculate the area of the triangle formed by these lines using determinants.
The formula for the area of a triangle formed by three points (x1, y1), (x2, y2), and (x3, y3) is:
Area = |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| / 2
In this case, the three points are (7, 0), (3, 0), and the x-intercept of the first line.
Calculating the determinant, we get:
Area = |7(0 - (5/7)(0)) + 3((5/7)(0) - 0) + x(0 - 0)| / 2
= |0 + 0 + 0| / 2
= 0 / 2
= 0
Therefore, the area of the triangle formed by the lines 5x - 7y = 35, 4x - 3y = 12, and the x-axis is 0 square units.
Hence, none of the given options (a), (b), (c), or (d) is correct.
We have two equations:
1. 5x - 7y = 35
2. 4x - 3y = 12
First, let's find the intersection points of these two lines.
Solving these equations simultaneously, we get:
1. 5x - 7y = 35 => y = (5x - 35)/7 => y = (5/7)x - 5
2. 4x - 3y = 12 => y = (4x - 12)/3 => y = (4/3)x - 4
Setting y = 0 in both equations, we can find the x-intercepts of the lines:
1. (5/7)x - 5 = 0 => (5/7)x = 5 => x = 7
2. (4/3)x - 4 = 0 => (4/3)x = 4 => x = 3
So the intersection points are (7, 0) and (3, 0).
Now, let's find the equation of the third line, which is the x-axis. The equation of the x-axis is y = 0.
We can now calculate the area of the triangle formed by these lines using determinants.
The formula for the area of a triangle formed by three points (x1, y1), (x2, y2), and (x3, y3) is:
Area = |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| / 2
In this case, the three points are (7, 0), (3, 0), and the x-intercept of the first line.
Calculating the determinant, we get:
Area = |7(0 - (5/7)(0)) + 3((5/7)(0) - 0) + x(0 - 0)| / 2
= |0 + 0 + 0| / 2
= 0 / 2
= 0
Therefore, the area of the triangle formed by the lines 5x - 7y = 35, 4x - 3y = 12, and the x-axis is 0 square units.
Hence, none of the given options (a), (b), (c), or (d) is correct.
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