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24 Jul 2019, 09:48
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
33% (02:16) correct
67%
(02:30)
wrong
based on 90
sessions
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Perimeter of a triangle with integer sides is equal to 15. How many such triangles are possible?
A. 7
B. 6
C. 8
D. 5
E. 4
A. 7
B. 6
C. 8
D. 5
E. 4
25 Jul 2019, 07:03
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Dillesh4096
Concept: If a, b & c are 3 integer sides of a triangle, "Difference of any 2 sides < Third side < Sum of the 2 sides"
Assume a ≤ b ≤ c,
If a = 1, Possible triangle is (a, b, c) = (1, 7, 7)
If a = 2, possible triangle is (a, b, c) = (2, 6, 7)
If a = 3, possible triangles are (a, b, c) = (3, 6, 6) and (3, 5, 7)
If a = 4, possible triangles are (a, b, c) = (4, 4, 7) and (4, 5, 6)
If a = 5, possible triangle is (5, 5, 5)
So, Total 7 triangles are possible.
Option A
Pls Hit Kudos if you like the solution
Updated on: 28 Jul 2019, 21:50
Originally posted by himanshu14 on 27 Jul 2019, 10:23.
Last edited by himanshu14 on 28 Jul 2019, 21:50, edited 1 time in total.
Last edited by himanshu14 on 28 Jul 2019, 21:50, edited 1 time in total.
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When perimeter is given as P.
if P=odd
No. of triangle =[(p+3)^2/48]
if P=even
No. of triangle =[(p)^2/48]
where [ ] is nearest integer function.
here P=15 (odd)
so no of triangle = [18*18/48]= [6.75]= 7
if P=odd
No. of triangle =[(p+3)^2/48]
if P=even
No. of triangle =[(p)^2/48]
where [ ] is nearest integer function.
here P=15 (odd)
so no of triangle = [18*18/48]= [6.75]= 7
