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Sagot :
As per given by the question,
There are given that a sides and length of the four triangle.
Now,
Check one-by-one, whether triangles are right triangle or not.
Then,
For check the triangle is right triangle or not, use pythagoras theorem.
Now,
For first triangle,
The side is given,
Suppose ,
[tex]A=12,\text{ B=24, and C=}\sqrt[]{439}[/tex]Then,
From the pythagoras theorem,
[tex]A^2+B^2=C^2[/tex]Put the value of A, B, and C in above formula;
So,
[tex]\begin{gathered} 12^2+24^2=(\sqrt[]{439})^2 \\ 144+576=439 \\ 720\ne439 \end{gathered}[/tex]Hence, first triangle is not a right angle triangle.
Now,
For second triangle,
[tex]A=14,\text{ B=18, and C=}\sqrt[\square]{520}[/tex]Then,
[tex]\begin{gathered} A^2+B^2=C^2 \\ 14^2+18^2=(\sqrt[]{520})^2 \\ 196+324=520 \\ 520=520 \end{gathered}[/tex]Hence, the second triangle is right angle triangle.
Now,
For third triangle,
[tex]\begin{gathered} A^2+B^2=C^2 \\ 16^2+18^2=(\sqrt[]{421})^2 \\ 256+324=421 \\ 580\ne421 \end{gathered}[/tex]Hence, the third triangle is not a right angle triangle.
Now,
For fourth triangle,
[tex]\begin{gathered} A^2+B^2=C^2 \\ 15^2+18^2=(\sqrt[]{549})^2 \\ 225+324=549 \\ 549=549 \end{gathered}[/tex]Hence, the fourth triangle is also a right triangle.
So,
The second and fourth triangle is right angle triangle.
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