determine whether a triangle with the given side lengths is a right triangle.

Question

Accepted Answer

# Explanation:
## Step1: Apply Pythagorean theorem
For a triangle with side lengths $a$, $b$, $c$ ($c$ is the longest side), check if $a^{2}+b^{2}=c^{2}$

### (a) For $a = 6$, $b = 8$, $c = 10$
$$
\begin{align*}
a^{2}+b^{2}&=6^{2}+8^{2}\
&=36 + 64\
&=100
\end{align*}
$$
$$
c^{2}=10^{2}=100
$$
Since $a^{2}+b^{2}=c^{2}$, it is a right - triangle.

### (b) For $a = 14$, $b = 48$, $c = 50$
$$
\begin{align*}
a^{2}+b^{2}&=14^{2}+48^{2}\
&=196+2304\
&=2500
\end{align*}
$$
$$
c^{2}=50^{2}=2500
$$
Since $a^{2}+b^{2}=c^{2}$, it is a right - triangle.

### (c) For $a = 10$, $b = 12$, $c = 16$
$$
\begin{align*}
a^{2}+b^{2}&=10^{2}+12^{2}\
&=100 + 144\
&=244
\end{align*}
$$
$$
c^{2}=16^{2}=256
$$
Since $a^{2}+b^{2}
eq c^{2}$, it is not a right - triangle.

### (d) For $a = 9$, $b = 13$, $c = 16$
$$
\begin{align*}
a^{2}+b^{2}&=9^{2}+13^{2}\
&=81+169\
&=250
\end{align*}
$$
$$
c^{2}=16^{2}=256
$$
Since $a^{2}+b^{2}
eq c^{2}$, it is not a right - triangle.

# Answer:
(a) Right triangle
(b) Right triangle
(c) Not a right triangle
(d) Not a right triangle

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QUESTION IMAGE

Question

Explanation:

Step1: Apply Pythagorean theorem

(a) For \(a = 6\), \(b = 8\), \(c = 10\)

(b) For \(a = 14\), \(b = 48\), \(c = 50\)

(c) For \(a = 10\), \(b = 12\), \(c = 16\)

(d) For \(a = 9\), \(b = 13\), \(c = 16\)

Answer: