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pythagorean triplet
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Math Problems
Grade 7
Least common multiple
Full solution
Q.
pythagorean triplet
List Triplets Pattern:
List the first few Pythagorean triplets to identify a pattern.
3
−
4
−
5
3-4-5
3
−
4
−
5
,
5
−
12
−
13
5-12-13
5
−
12
−
13
,
7
−
24
−
25
7-24-25
7
−
24
−
25
, ...
Choose Simplest Triplet:
Choose the simplest triplet to work with, like
3
3
3
-
4
4
4
-
5
5
5
. Check if
3
2
+
4
2
=
5
2
3^2 + 4^2 = 5^2
3
2
+
4
2
=
5
2
.
Calculate Squares:
Calculate
3
2
3^2
3
2
and
4
2
4^2
4
2
.
\newline
3
2
=
9
3^2 = 9
3
2
=
9
,
4
2
=
16
4^2 = 16
4
2
=
16
.
Add Squares:
Add the squares together.
9
+
16
=
25
9 + 16 = 25
9
+
16
=
25
.
Compare to
5
2
5^2
5
2
:
Compare the sum to
5
2
5^2
5
2
.
\newline
5
2
=
25
5^2 = 25
5
2
=
25
.
Verify Equality:
Verify if
25
25
25
equals
25
25
25
.
\newline
Yes, it does, so
3
−
4
−
5
3-4-5
3
−
4
−
5
is a Pythagorean triplet.
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