Chapter 5.5, Problem 27PSB

To determine

To find: The length of $\overline{RH}$ to the nearest tenth.

Answer to Problem 27PSB

  $RH=22.7$

Explanation of Solution

Given information:

RHOM is a rhombus.

  

$\begin{array}{l}m\angle MBR=21x+13,MR=6.2x\\ \end{array}$

Calculation:

RHOM is a rhombus.

  

  $\begin{array}{l}\text{In above figure,}\\ \text{RHOM is a rhombus}\\ m\angle MBR=21x+13\\ \Rightarrow 90=21x+13\left\{\text{Diagonals are perpendicular bisector of each other in rhombus}\right\}\\ \Rightarrow x=\frac{77}{21}\\ \Rightarrow MR=6.2x\\ \Rightarrow MR=6.2\left(\frac{77}{21}\right)\\ \Rightarrow MR=22.7\\ \Rightarrow RH=MR=22.7\left\{\text{All sides are equal in rhombus}\right\}\end{array}$