Hello!
To check if the triangles are right triangles, we must use the Pythagoras Theorem.
[tex]a^2=b^2+c^2[/tex]
We will consider the biggest side as A, and the other smallest sides as B and C, look:
Triangle A: is a right triangle.
[tex]\begin{gathered} a^2=b^2+c^2 \\ (\sqrt{5})^2=(\sqrt{2})^2+(\sqrt{3})^2 \\ \sqrt{5}\cdot\sqrt{5}=\sqrt{2}\cdot\sqrt{2}+\sqrt{3}\cdot\sqrt{3} \\ \sqrt{25}=\sqrt{4}+\sqrt{9} \\ 5=2+3 \\ 5=5 \end{gathered}[/tex]
Triangle B: isn't a right triangle.
[tex]\begin{gathered} \begin{equation*} a^2=b^2+c^2 \end{equation*} \\ (\sqrt{5})^2=(\sqrt{3})^2+(\sqrt{4})^2 \\ 5=3+4 \\ 57 \end{gathered}[/tex]
Triangle C: isn't a right triangle.
[tex]\begin{gathered} \begin{equation*} a^2=b^2+c^2 \end{equation*} \\ 6^2=4^2+5^2 \\ 36=16+25 \\ 3641 \end{gathered}[/tex]
Triangle D: isn't a right triangle.
[tex]\begin{gathered} \begin{equation*} a^2=b^2+c^2 \end{equation*} \\ 7^2=5^2+5^2 \\ 49=25+25 \\ 4950 \end{gathered}[/tex]
Triangle E: is a right triangle.
[tex]\begin{gathered} \begin{equation*} a^2=b^2+c^2 \end{equation*} \\ 10^2=8^2+6^2 \\ 100=64+36 \\ 100=100 \end{gathered}[/tex]
Answer:
A and E are right triangles.
