15.9k views
2 votes
Select all the right triangles, given the lengths of the sides sa ve 5

Select all the right triangles, given the lengths of the sides sa ve 5-example-1
User Pbalaga
by
8.2k points

1 Answer

4 votes

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

User Anwesha
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories