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08 Jan 2022, 12:29
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In the given figure ABCD is a rectangle and the side lengths are integers. The perimeter of the rectangle is 48 and AB is parallel to the x-axis. If AB – BC < 4, which of the following can be the co-ordinate of C?
I. (16, 17)
II. (16, 15)
III. (17,16)
A. I only
B. II only
C. III only
D. I and III
E. I , II, and III
18 Jan 2022, 23:00
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In the given figure ABCD is a rectangle and the side lengths are integers. The perimeter of the rectangle is 48 and AB is parallel to the x-axis. If AB – BC < 4, which of the following can be the co-ordinate of C?
I. (16, 17)
II. (16, 15)
III. (17,16)
A. I only
B. II only
C. III only
D. I and III
E. I , II, and III[/quote]
2*(AB+BC) =48..So, (AB+BC)=24...i.e., BC=24-AB..eqn 1
Given, AB-BC < 4
substituting eqn 1...
AB-(24-AB) < 4
AB<14.
Now, as sides are integers(given), max value of AB =13. When AB=13, BC =24-13 =11. Then, C = (4+13,5+11) =(17,16)..No. III
When AB=12, BC =24-12 =12. Then, C = (4+12,5+12) =(16,17)..No. I...
Now, if I is correct, II cannot be.
So, I & III is possible.
Option D
I. (16, 17)
II. (16, 15)
III. (17,16)
A. I only
B. II only
C. III only
D. I and III
E. I , II, and III[/quote]
2*(AB+BC) =48..So, (AB+BC)=24...i.e., BC=24-AB..eqn 1
Given, AB-BC < 4
substituting eqn 1...
AB-(24-AB) < 4
AB<14.
Now, as sides are integers(given), max value of AB =13. When AB=13, BC =24-13 =11. Then, C = (4+13,5+11) =(17,16)..No. III
When AB=12, BC =24-12 =12. Then, C = (4+12,5+12) =(16,17)..No. I...
Now, if I is correct, II cannot be.
So, I & III is possible.
Option D
04 Jul 2022, 03:29
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if we consider the choices individually
I. (16, 17)
this means that length of \(AB = \sqrt{ (16-4)^2- (5-5)^2} = 12\)
ans length of BC = Y Cordinate of C - Y cordinate of \(B = 17-5=12 \)
These values of AB and BC satisfy the AB – BC < 4 and perimeter=48
II. (16, 15)
this means that length of \(AB = \sqrt{ (16-4)^2- (5-5)^2} = 12\)
ans length of BC = Y Cordinate of C - Y cordinate of \(B = 15-5=10\)
These values of AB and BC do not satisfy perimeter=48
III. (17,16)
this means that length of \(AB = \sqrt{ (17-4)^2- (5-5)^2} = 13\)
ans length of BC = Y Cordinate of C - Y cordinate of \(B = 16-5=11\)
These values of AB and BC satisfy the AB – BC < 4 and perimeter=48
only I and III satisfy both the conditions.
I. (16, 17)
this means that length of \(AB = \sqrt{ (16-4)^2- (5-5)^2} = 12\)
ans length of BC = Y Cordinate of C - Y cordinate of \(B = 17-5=12 \)
These values of AB and BC satisfy the AB – BC < 4 and perimeter=48
II. (16, 15)
this means that length of \(AB = \sqrt{ (16-4)^2- (5-5)^2} = 12\)
ans length of BC = Y Cordinate of C - Y cordinate of \(B = 15-5=10\)
These values of AB and BC do not satisfy perimeter=48
III. (17,16)
this means that length of \(AB = \sqrt{ (17-4)^2- (5-5)^2} = 13\)
ans length of BC = Y Cordinate of C - Y cordinate of \(B = 16-5=11\)
These values of AB and BC satisfy the AB – BC < 4 and perimeter=48
only I and III satisfy both the conditions.
