Answer:
Yes
12, 35, 37
16, 30, 34
20, 21, 29
No
18, 24, 42
Step-by-step explanation:
Required
Determine which length form a right triangle
To do this, we make use of Pythagoras theorem where the square of the largest length = the sum of the squares of the other lengths
So:
(1) 12, 35, 37 --- Yes
[tex]37^2 = 35^2 + 12^2[/tex]
[tex]1369 = 1225 + 144[/tex]
[tex]1369 = 1369[/tex]
(2) 16, 30, 34 --- Yes
[tex]34^2 = 16^2 + 30^2[/tex]
[tex]1156 = 256 + 900[/tex]
[tex]1156 = 1156[/tex]
(3) 18, 24, 42 --- No
[tex]42^2 =18^2 + 24^2[/tex]
[tex]1764 =324 + 576[/tex]
[tex]1764 =900[/tex]
[tex]1764 \ne 900[/tex]
(4) 20, 21, 29 -- Yes
[tex]29^2 = 20^2 + 21^2[/tex]
[tex]841= 400 + 441[/tex]
[tex]841= 841[/tex]
Based on the Pythagorean Triple, "12, 35, 37", "16, 30, 34" and "20, 21, 29" will form a right triangle(YES), while "18, 24, 42" will not (NO).
The Pythagorean triple can be described as any three set of integers representing sides of a right triangle that are solutions to the Pythagorean Theorem, which is given as:
c² = a² + b².
c is the longest side of the right triangle or largest of the set of integers of the Pythagorean triple.
Thus, find out which set of lengths will form a right triangle:
12, 35, 37 will form a right triangle, because:
37² = 35² + 12²
1,369 = 1,369
Also, the rest set of lengths will form a right triangle except, "18, 24, 42".
Thus, based on the Pythagorean Triple, "12, 35, 37", "16, 30, 34" and "20, 21, 29" will form a right triangle(YES), while "18, 24, 42" will not (NO).
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