Question

Find five rational number between -2 and -3.
Please answer it.
​

Answer 1

Step-by-step explanation:

know, sum of any two sides of a triangle is greater than the third side.

\begin{gathered}\sf \: \implies \: OD + OC > CD - - - (3) \\ \\ \end{gathered}

⟹OD+OC>CD−−−(3)

In \triangle△ OAD

We know, sum of any two sides of a triangle is greater than the third side.

\begin{gathered}\sf \: \implies \: OD + OA > AD - - - (4) \\ \\ \end{gathered}

⟹OD+OA>AD−−−(4)

On adding equation (1), (2), (3) and (4), we get

\begin{gathered}\sf \: 2(OA + OB +OC + OD) > AB + BC + CD + AD \\ \\ \end{gathered}

2(OA+OB+OC+OD)>AB+BC+CD+AD

\begin{gathered}\sf \: 2(OA + OC + OB + OD) > AB + BC + CD + AD \\ \\ \end{gathered}

2(OA+OC+OB+OD)>AB+BC+CD+AD

\begin{gathered}\sf \: 2(AC + BD) > AB + BC + CD + AD \\ \\ \end{gathered}

2(AC+BD)>AB+BC+CD+AD

\begin{gathered}\sf \:\sf \: \implies \: AB + BC + CD + AD < 2(AC + BD) \\ \\ \end{gathered}

⟹AB+BC+CD+AD<2(AC+BD)

Hence, the given statement is true and justified.