Chapter 6.4, Problem 15CE

To determine

To Find: The length of the diagonals.

Answer to Problem 15CE

The length of the diagonals of the parallelogram is less than 22.

  $AC<22\text{ and }BD<22$ .

Explanation of Solution

Given information:

Two sides of a parallelogram have lengths 10 and 12.

Consider the triangle is shown below:

  

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

  $\begin{array}{l}AB+BC>AC\hfill \\ AB+AC>BC\hfill \\ AC+BC>AB\hfill \end{array}$

The $\left|\right|gm$ can be drawn as shown below:

  

As it can be seen that the two sides are given so using above figure;

Therefore,

  $\begin{array}{l}AB+BC>AC\hfill \\ 10 +12>AC\hfill \\ 22>AC\hfill \\ AC<22\hfill \end{array}$

Similarly finding the BD,

Using the same theorem,

  $\begin{array}{cc}AB+AD& >BD\\ 10+12& >BD\\ 22& >BD\\ BD& <22\end{array}$

It can be observe that the diagonals of the parallelogram will have value less than 22.

Therefore, $AC<22\text{ and }BD<22$