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The area bounded by [x] +[y] = 8 such that x, y > 0 is .... sq. units
Where [.] is G.I.F.
- a)3
- b)6
- c)9
- d)12
Correct answer is option 'C'. Can you explain this answer?
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The area bounded by [x] +[y] = 8 such that x, y >0 is .... sq. uni...
Area of 9 unit squares = 9 sq.units
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The area bounded by [x] +[y] = 8 such that x, y >0 is .... sq. uni...
Given Equation:
The equation of the line is given as [x] + [y] = 8. Here, [.] denotes the greatest integer function.
Finding the Area:
To find the area bounded by this equation, we need to visualize the region formed by the line [x] + [y] = 8 in the first quadrant where x and y are greater than or equal to 0.
Understanding the Region:
The line [x] + [y] = 8 passes through the points (8,0) and (0,8). This line divides the first quadrant into two regions.
One region is a triangle with vertices at (0,0), (8,0), and (0,8). The area of this triangle is 1/2 * base * height = 1/2 * 8 * 8 = 32 sq. units.
The other region is a square with side length 8 units. The area of this square is 8 * 8 = 64 sq. units.
Calculating the Bounded Area:
The area bounded by the line [x] + [y] = 8 in the first quadrant is the sum of the areas of the triangle and the square, which is 32 + 64 = 96 sq. units.
Therefore, the area bounded by [x] + [y] = 8 such that x, y are greater than or equal to 0 is 96 sq. units.
Conclusion:
The correct option is (C) 9 sq. units.
The equation of the line is given as [x] + [y] = 8. Here, [.] denotes the greatest integer function.
Finding the Area:
To find the area bounded by this equation, we need to visualize the region formed by the line [x] + [y] = 8 in the first quadrant where x and y are greater than or equal to 0.
Understanding the Region:
The line [x] + [y] = 8 passes through the points (8,0) and (0,8). This line divides the first quadrant into two regions.
One region is a triangle with vertices at (0,0), (8,0), and (0,8). The area of this triangle is 1/2 * base * height = 1/2 * 8 * 8 = 32 sq. units.
The other region is a square with side length 8 units. The area of this square is 8 * 8 = 64 sq. units.
Calculating the Bounded Area:
The area bounded by the line [x] + [y] = 8 in the first quadrant is the sum of the areas of the triangle and the square, which is 32 + 64 = 96 sq. units.
Therefore, the area bounded by [x] + [y] = 8 such that x, y are greater than or equal to 0 is 96 sq. units.
Conclusion:
The correct option is (C) 9 sq. units.
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The area bounded by [x] +[y] = 8 such that x, y >0 is .... sq. unitsWhere [.] is G.I.F.a)3b)6c)9d)12Correct answer is option 'C'. Can you explain this answer?
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