Chapter 16.3, Problem 3PS

To determine

To find: Themeasure of the parallelogram’s longer diagonal.

Answer to Problem 3PS

The measure of the parallelogram’s longer diagonalis $7\text{unit}$ .

Explanation of Solution

Given information:

The length of the sides of the parallelogram are $7$ and $9$ . The measure of its shorter diagonal is $8$ .

The value of $y$ in the given figure is calculated as by using Stewart’s Theorem,

  $\begin{array}{l}{\left(7\right)}^{2}x+{\left(9\right)}^{2}x={\left(4\right)}^2\left(2x\right)+2x\left(x\right)\left(x\right)\\ 49x+81x=32x+2x^3\\ x^3=49x\\ x=7\text{unit}\end{array}$

Thus, the measure of the parallelogram’s longer diagonal is $7\text{unit}$ .