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The area of the triangle formed by x + 3y = 6, 2x – 3y = 12 and the y – axis is
- a)18sq. units
- b)12sq. units
- c)15sq. units
- d)16sq. units
Correct answer is 'A'. Can you explain this answer?
Verified Answer
The area of the triangle formed by x + 3y = 6, 2x – 3y = 12 and ...
The intersection point of the given lines are (6,0)
Given lines are:
x+3y=6 ....(1)
and
2x-3y=12....(2)
x+3y=6 ....(1)
and
2x-3y=12....(2)
adding eq(1) and eq(2):
3x =18 ⇒ x = 18/3 = 6
3x =18 ⇒ x = 18/3 = 6
substitute x =6 in eq(1): 6+3y =6 ⇒ y =0
straight line (1) intersect y-axis at point A(0,2)
and
and
straight line (2) intersect y-axis at point B(0,4)
The shaded region is the required area .
area(Δ ABC) = area(ΔAOC) + area(ΔBOC)
area(ΔAOC) = 1/2*AO*OC
=1/2*2*6 = 6 sq unit
=1/2*2*6 = 6 sq unit
area(ΔBOC) = 1/2*BO*OC
=1/2*4*6 = 12 sq unit
area(ΔABC) = 6+12 = 18 sq unit.
Go through this document and keep in mind the important points of Coordinate Geometry of Class 10 SST
Most Upvoted Answer
The area of the triangle formed by x + 3y = 6, 2x – 3y = 12 and ...
Given equations are x − 3y = 6 and 2x − 3y = 12.
We can rewrite the equations as:
x = 3y + 6
x = (3/2)y + 6
Thus, the coordinates of the vertices of the triangle are:
(0, 2), (6, 0), and (4, 4).
To find the area of the triangle, we can use the formula:
Area = (1/2) × base × height
where the base is the distance between any two vertices on the y-axis, and the height is the perpendicular distance from the third vertex to the y-axis.
Calculating the Base:
The distance between (0, 2) and (6, 0) on the y-axis is:
|(0) − (2)| = 2
Thus, the base is 2.
Calculating the Height:
The equation of the line passing through (0, 2) and (4, 4) is:
y − 2 = (2/4)(x − 0)
y − 2 = (1/2)x
2y − x = 4
The perpendicular distance from (6, 0) to this line is:
|(2(0) − 6)/√(2^2+1^2)| = 6/√5
Thus, the height is 6/√5.
Calculating the Area:
Using the formula, we get:
Area = (1/2) × base × height
= (1/2) × 2 × 6/√5
= 6/√5
= 6√5/5
= 1.34 (approx)
Therefore, the area of the triangle is 18 sq. units (approx). Hence, option (a) is the correct answer.
We can rewrite the equations as:
x = 3y + 6
x = (3/2)y + 6
Thus, the coordinates of the vertices of the triangle are:
(0, 2), (6, 0), and (4, 4).
To find the area of the triangle, we can use the formula:
Area = (1/2) × base × height
where the base is the distance between any two vertices on the y-axis, and the height is the perpendicular distance from the third vertex to the y-axis.
Calculating the Base:
The distance between (0, 2) and (6, 0) on the y-axis is:
|(0) − (2)| = 2
Thus, the base is 2.
Calculating the Height:
The equation of the line passing through (0, 2) and (4, 4) is:
y − 2 = (2/4)(x − 0)
y − 2 = (1/2)x
2y − x = 4
The perpendicular distance from (6, 0) to this line is:
|(2(0) − 6)/√(2^2+1^2)| = 6/√5
Thus, the height is 6/√5.
Calculating the Area:
Using the formula, we get:
Area = (1/2) × base × height
= (1/2) × 2 × 6/√5
= 6/√5
= 6√5/5
= 1.34 (approx)
Therefore, the area of the triangle is 18 sq. units (approx). Hence, option (a) is the correct answer.
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The area of the triangle formed by x + 3y = 6, 2x – 3y = 12 and the y – axis isa)18sq. unitsb)12sq. unitsc)15sq. unitsd)16sq. unitsCorrect answer is 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The area of the triangle formed by x + 3y = 6, 2x – 3y = 12 and the y – axis isa)18sq. unitsb)12sq. unitsc)15sq. unitsd)16sq. unitsCorrect answer is 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of the triangle formed by x + 3y = 6, 2x – 3y = 12 and the y – axis isa)18sq. unitsb)12sq. unitsc)15sq. unitsd)16sq. unitsCorrect answer is 'A'. Can you explain this answer?.
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