Chapter 6, Problem 41SGR

To determine

The length of GH.

Answer to Problem 41SGR

  $GH=19.2$

Explanation of Solution

Given:

Given figure is a kite.

Calculation:

According to the Kite Theorem,

  $\overline{GJ}\perp \overline{FH}$

Therefore, angle GUH is a right angle and hence, the triangle GUH is a right triangle.

So,

  $\begin{array}{l}GH=\sqrt{{\left(UG\right)}^2+{\left(UH\right)}^2}\\ GH=\sqrt{{\left(12\right)}^2+{\left(15\right)}^2}\\ GH=\sqrt{369}\\ GH\approx 19.2\\ GH=19.2\end{array}$