Question

Which could be lengths of the sides of a right.....

Answer 1

The length of sides of a right triangle always satisfy the pythagoras theorem.

Apply the pythagoras theorem to each sides of triangle.

`\begin{gathered} (63)^2=(31)^2+(32)^2 \\ 3969=961+1024 \\ 3969\\e1985 \end{gathered}`

Length of sides not belong to a right triangle.

For second option,

`\begin{gathered} (53)^2=(28)^2+(45)^2 \\ 2809=784+2025 \\ 2809=2809 \end{gathered}`

Pythagoras theorem satisfied. Sides belongs to a right triangle.

Third option,

`\begin{gathered} (64)^2=(36)^2+(49)^2 \\ 4096=1296+2401 \\ 4096\\e3697 \end{gathered}`

Sides not belongs to a right triangle.

Fouth option,

`\begin{gathered} (169)^2=(5)^2+(12)^2 \\ 28561=25+144 \\ 28561\\e169 \end{gathered}`

Sides not belong to a right triangle.

So possible length of a right triangle is 28, 45, 53.