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30 Dec 2019, 06:58
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Difficulty:
65%
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Question Stats:
51% (02:10) correct
49%
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wrong
based on 41
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Q. A right angled triangle having its sides as 6,8, and 10 and has its perimeter and area numerically equal. How many other right angled triangles, having all their sides integers, satisfy the given property?
A. 3
B. 1
C. 4
D. 2
E. Infinitely many
A. 3
B. 1
C. 4
D. 2
E. Infinitely many
31 Dec 2019, 21:24
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Solved it using variables but i think there has to be an easier way to solve this.
PFA the solution!
Hope it helps!
PFA the solution!
Hope it helps!
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10 Apr 2024, 11:24
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Pythagorean triples can be generated by:
a= (m^2-n^2)
b= 2mn
c= (m^2+n^2)
where m>n>0
So, with the given conditions, perimeter is:
a+b+c= 2m(m+n)
Area equals:
ab/2 = ((m^2-n^2)/2)2mn
Equating:
2m(m+n)=mn(m^2-n^2)
2(m+n)=n(m+n)(m-n) and:
n(m-n)=2
Since m and n are integers:
n=1, m=3 OR
n=2, m=3
Plugging n=1,m=3 into the triplets formula:
a=8,b=6 and c=10
Plugging n=2,m=3 into same:
a=5,b=12 and c=13
Since 6,8,10 was already identified, there is only:
1 other
Posted from my mobile device
a= (m^2-n^2)
b= 2mn
c= (m^2+n^2)
where m>n>0
So, with the given conditions, perimeter is:
a+b+c= 2m(m+n)
Area equals:
ab/2 = ((m^2-n^2)/2)2mn
Equating:
2m(m+n)=mn(m^2-n^2)
2(m+n)=n(m+n)(m-n) and:
n(m-n)=2
Since m and n are integers:
n=1, m=3 OR
n=2, m=3
Plugging n=1,m=3 into the triplets formula:
a=8,b=6 and c=10
Plugging n=2,m=3 into same:
a=5,b=12 and c=13
Since 6,8,10 was already identified, there is only:
1 other
Posted from my mobile device
