Chapter 6.6, Problem 77SPR

To determine

The value of MG.

Answer to Problem 77SPR

  $MG=9$

Explanation of Solution

Given:

DFGH is a rhombus.

  

  $HM=12,HD=15$

Calculation:

The diagonals of a rhombus are perpendicular.

Hence, $\overline{HF}\cong \overline{GD}.$

And by the definition of perpendicular lines, angle DMH is a right angle.

Consider the right triangle DMH:

  $\begin{array}{l}MD=\sqrt{{\left(HD\right)}^2-{\left(HM\right)}^2}\\ MD=\sqrt{{\left(15\right)}^2-{\left(12\right)}^2}\\ MD=\sqrt{81}\\ MD=9\end{array}$

Also, the diagonals of a rhombus bisect each other.

So,

  $\begin{array}{l}MG=DM\\ MG=9\end{array}$