Chapter 11.2, Problem 14PSB

To determine

To find the trianglewith largest area.

Answer to Problem 14PSB

All triangles have equal area.

Explanation of Solution

Given:

Lines $\overleftrightarrow{CF}$ and $\overleftrightarrow{AB}$ are parallel and 10mm apart.

  $\Delta ACB$ with height 10mm and base 16mm.

  $\Delta ADB$ with height 10mm and base 16mm.

  $\Delta AEB$ with height 10mm and base 16mm.

  $\Delta AFB$ with height 10mm and base 16mm.

Formula Used:

  $\begin{array}{l}Areaoftriangle=\frac{1}{2}\ast b\ast h\\ b=Base,\\ h=Height\end{array}$

Calculation:

  

All of the four triangles have same base and height, therefore there areas are equal.

  $\begin{array}{l}Areaoftriangle=\frac{1}{2}\ast b\ast h\\ A(\Delta ACB)=A(\Delta ADB)=A(\Delta AEB)=A(\Delta AFB)=\frac{1}{2}*16*10\\ =\frac{1}{2}*160\\ =80m{m}^2\end{array}$