Chapter 5.5, Problem 12PSA

To determine

To find: Thelength of ET to the nearest tenth.

Answer to Problem 12PSA

The value of $ET$ to the nearest tenth is 370.

Explanation of Solution

Given Information:

  $RECT$ is a rectangle

  $\begin{array}{l}RA=43x\\ AC=214x-742\end{array}$

Formula used:

The diagonals of a rectangle are equal and bisect each other.

Calculation:

  $RECT$ is a rectangle where $RC\text{and}ET$ are the diagonals.

We know that the diagonals of a rectangle are equal and bisect each other, then we have

  $RC=ET\mathrm{...}\left(\text{i}\right)$

Also, $RA=AC$

As $RA=43x\text{and}AC=214x-742$

  $\begin{array}{l}\Rightarrow 43x=214x-742\\ \Rightarrow 171x=742\\ \Rightarrow x=4.33\end{array}$

From (i), we have

  $\begin{array}{l}ET=RC=RA+AC\\ \Rightarrow ET=43x+214x-742\\ \Rightarrow ET=257x-742\\ \Rightarrow ET=370.81\end{array}$

Hence, the value of $ET$ to the nearest tenth is 370.