Question

Select all the right triangles, given the lengths of the sides sa ve 5

Answer 1

To know which triangle is a right triangle, we will have to apply the Pythagorean theorem to each of them.

According to the Pythagorean theorem, we have that:

`\text{adjacent}^2+opposite^2=hypothenus^2`

Now, we must check that this holds true for each triangle.

a) For the first triangle A, we have that:

`\begin{gathered} \text{adjacent}^2+opposite^2=hypothenus^2 \\ \Rightarrow(\sqrt[]{2})^2_{}+(\sqrt[]{3})^2=(\sqrt[]{5})^2 \\ \Rightarrow2+3=5 \\ \Rightarrow5=5 \end{gathered}`

Since both sides of the equation are the same, triangle A is a right triangle

b) For triangle B, we have that:

`\begin{gathered} \text{adjacent}^2+opposite^2=hypothenus^2 \\ \Rightarrow(\sqrt[]{3})^2_{}+(\sqrt[]{4})^2=(\sqrt[]{5})^2 \\ \Rightarrow3+4=5 \\ \Rightarrow7=5 \end{gathered}`

Since both sides of the equation are not the same, triangle B is NOT a right triangle

c) For triangle C, we have that:

`\begin{gathered} \text{adjacent}^2+opposite^2=hypothenus^2 \\ \Rightarrow(4)^2_{}+(5)^2=(6)^2 \\ \Rightarrow16+25=36 \\ \Rightarrow41=36 \end{gathered}`

Since both sides of the equation are not the same, triangle C is NOT a right triangle

d) For triangle D, we have that:

`\begin{gathered} \text{adjacent}^2+opposite^2=hypothenus^2 \\ \Rightarrow(5)^2_{}+(5)^2=(7)^2 \\ \Rightarrow25+25=49 \\ \Rightarrow50=49 \end{gathered}`

Since both sides of the equation are not the same, triangle D is NOT a right triangle

e) For triangle E, we have that:

`\begin{gathered} \text{adjacent}^2+opposite^2=hypothenus^2 \\ \Rightarrow(6)^2_{}+(8)^2=(10)^2 \\ \Rightarrow36+64=100 \\ \Rightarrow100=100 \end{gathered}`

Since both sides of the equation are the same, triangle E is a right triangle

Therefore, only triangles A and E are ri