Question

What are the right triangles in this picture given the side length:

Answer 1

Hello!

To check if the triangles are right triangles, we must use the Pythagoras Theorem.

`a^2=b^2+c^2`

We will consider the biggest side as A, and the other smallest sides as B and C, look:

Triangle A: is a right triangle.

`\begin{gathered} a^2=b^2+c^2 \\ (√(5))^2=(√(2))^2+(√(3))^2 \\ √(5)\cdot√(5)=√(2)\cdot√(2)+√(3)\cdot√(3) \\ √(25)=√(4)+√(9) \\ 5=2+3 \\ 5=5 \end{gathered}`

Triangle B: isn't a right triangle.

`\begin{gathered} \begin{equation*} a^2=b^2+c^2 \end{equation*} \\ (√(5))^2=(√(3))^2+(√(4))^2 \\ 5=3+4 \\ 57 \end{gathered}`

Triangle C: isn't a right triangle.

`\begin{gathered} \begin{equation*} a^2=b^2+c^2 \end{equation*} \\ 6^2=4^2+5^2 \\ 36=16+25 \\ 3641 \end{gathered}`

Triangle D: isn't a right triangle.

`\begin{gathered} \begin{equation*} a^2=b^2+c^2 \end{equation*} \\ 7^2=5^2+5^2 \\ 49=25+25 \\ 4950 \end{gathered}`

Triangle E: is a right triangle.

`\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}`

Answer:

A and E are right triangles.