Chapter 12.2, Problem 29HP

To determine

To find: the dimensions of triangular prism

Answer to Problem 29HP

The dimensions are base 4 inches, height 2 inches of the triangular and the length of the prism is 11 inches.

Explanation of Solution

Given:

Volume is 44 cubic inches

  

Calculation:

The objective is to find the dimension of any triangular prism whose volume is 44 cubic inches. The volume V of a triangular prism is given by the formula

  $V=Bh$

Where B is the area of a triangle and h is the height which is the length of the prism

The area B is a triangle whose base is b and height is a .

The area B of the triangle is given by

  $B=\frac{1}{2}\cdot b\cdot a\text{ Where }b\text{ is the base and }a\text{ is the height of the triangle}$

Thus, the volume V of a triangular prism is

  $\begin{array}{l}V=Bh\\ 44=\frac{1}{2}abh\\ \text{44}=\frac{1}{2}abh\\ 44\cdot 2=2\cdot \frac{1}{2}abh\left[\text{Multiply both sides by 2}\right]\\ 88=abh\\ abh=88\end{array}$

Take $b=4$ then

  $\begin{array}{l}4ah=88\\ ah=\frac{88}{4}\\ \text{ =22}\\ \text{ =2}\cdot \text{11}\end{array}$

Thus, the dimension of a triangular prism whose volume is 44 cubic inches are base 4 inches, height 2 inches of the triangular and the length of the prism is 11 inches.

Conclusion:

Therefore, thedimensions are base 4 inches, height 2 inches of the triangular and the length of the prism is 11 inches.