Chapter 11.2, Problem 19PPS

To determine

To find: The value of given unknown variable.

Answer to Problem 19PPS

  $x=3.1$

Explanation of Solution

Given information:

  $\Delta FGI\cong \Delta LKM$

Concept and Formula Used:

The concept of congruent triangles is used. Two triangles are said to be congruent if their corresponding sides and the corresponding angles are equal.

We also use pythagoras theorem

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

Also, we use $\sqrt{5}=2.2$

Calculation:

As given that . $\Delta FGI\cong \Delta LKM$ , and we know that the two triangles are congruent if their parts are congruent, so we have $F\leftrightarrow L,G\leftrightarrow K,I\leftrightarrow M$ , therefore the corresponding sides are equal, so we have

  $LK=FG=2x+4$ . Now using pthagoras theorem in $\Delta FGI$ , we get

  $\begin{array}{l}{\left(FG\right)}^2={\left(FI\right)}^2+{\left(IG\right)}^2\\ {\left(FG\right)}^2={\left(5\right)}^2+{\left(10\right)}^2\\ {\left(FG\right)}^2=25+100\\ {\left(FG\right)}^2=125\end{array}$

Taking square root both the sides, we get

  $FG=5\sqrt{5}=5\left(2.2\right)=10.1cm$

Thus, we have

  $\begin{array}{l}2x+4=10.1\\ 2x=10.1-4\\ 2x=6.1\\ x=\frac{6.1}{2}=3.05~3.1\end{array}$

Conclusion:

  $x=3.1$