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Rectangle ABCD is constructed in the xy-plane so that sides AB and CD are parallel to the x-axis. Both the x and y coordinates of all four vertices of the rectangle are integers. How many rectangles can be constructed if x and y coordinates satisfy the inequality 11 < x < 29 and 5 ≤ y ≤ 13?
- a)153
- b)153C4
- c)4896
- d)2448
- e)5508
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Rectangle ABCD is constructed in the xy-plane so that sides AB and CD ...
Sides AB and CD are parallel to x-axis.
So, AD and BC will be parallel to y-axis.
So, AD and BC will be parallel to y-axis.
The x-coordinates take values from 12 to 28.
We can draw lines parallel to y-axis corresponding to each of these values.
So, we will be able to draw 17 vertical lines.
We can draw lines parallel to y-axis corresponding to each of these values.
So, we will be able to draw 17 vertical lines.
The y-coordinates take values from 5 to 13.
We can draw lines parallel to x-axis corresponding to each of these values.
So, we will be able to draw 9 horizontal lines.
We can draw lines parallel to x-axis corresponding to each of these values.
So, we will be able to draw 9 horizontal lines.
2 horizontal lines and two vertical lines will form a rectangle
Number of ways of selecting 2 horizontal lines from 9 horizontal lines = 9C2
9C2 = 9×8 / 2= 36
Number of ways of selecting 2 horizontal lines from 9 horizontal lines = 9C2
9C2 = 9×8 / 2= 36
Number of ways of selecting 2 veritcal lines from 17 vertical lines = 17C2
9C2 = 17×16 / 2 = 136
9C2 = 17×16 / 2 = 136
Number of rectangles that can be formed
Product of the number of ways of selecting 2 horizontal lines and number of ways of selecting two vertical lines
= 36 × 136 = 4896
= 36 × 136 = 4896
Choice C is the correct answer.
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Community Answer
Rectangle ABCD is constructed in the xy-plane so that sides AB and CD ...
Sides AB and CD are parallel to x-axis.
So, AD and BC will be parallel to y-axis.
So, AD and BC will be parallel to y-axis.
The x-coordinates take values from 12 to 28.
We can draw lines parallel to y-axis corresponding to each of these values.
So, we will be able to draw 17 vertical lines.
We can draw lines parallel to y-axis corresponding to each of these values.
So, we will be able to draw 17 vertical lines.
The y-coordinates take values from 5 to 13.
We can draw lines parallel to x-axis corresponding to each of these values.
So, we will be able to draw 9 horizontal lines.
We can draw lines parallel to x-axis corresponding to each of these values.
So, we will be able to draw 9 horizontal lines.
2 horizontal lines and two vertical lines will form a rectangle
Number of ways of selecting 2 horizontal lines from 9 horizontal lines = 9C2
9C2 = 9×8 / 2= 36
Number of ways of selecting 2 horizontal lines from 9 horizontal lines = 9C2
9C2 = 9×8 / 2= 36
Number of ways of selecting 2 veritcal lines from 17 vertical lines = 17C2
9C2 = 17×16 / 2 = 136
9C2 = 17×16 / 2 = 136
Number of rectangles that can be formed
Product of the number of ways of selecting 2 horizontal lines and number of ways of selecting two vertical lines
= 36 × 136 = 4896
= 36 × 136 = 4896
Choice C is the correct answer.
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Rectangle ABCD is constructed in the xy-plane so that sides AB and CD are parallel to the x-axis. Both the x and y coordinates of all four vertices of the rectangle are integers. How many rectangles can be constructed if x and y coordinates satisfy the inequality 11 < x < 29 and 5 ≤ y ≤ 13?a)153b)153C4c)4896d)2448e)5508Correct answer is option 'C'. Can you explain this answer?
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