Chapter 8.7, Problem 48HP

To determine

The formula for A , area of a geometric figure for triangle and to solve formula for variable other than A, that is b.

Answer to Problem 48HP

  $A=\frac{1}{2}bh$

  $b=2\frac{A}{h}$

Explanation of Solution

Given information:

Area of geometric figure such as triangle

Calculation:

Consider a triangle with base length b and height h . So, the area of the of the triangle is given by

  $\begin{array}{c}\text{Area of triangle}=\frac{1}{2}\left(\text{Base length }\times \text{ Height}\right)\\ A=\frac{1}{2}bh\end{array}$

Now in order to solve for the variable b , first multiply both sides by 2 and then divide both sides by h to simplify further as shown below:

  $\begin{array}{l}A=\frac{1}{2}bh\\ A\left(2\right)=\frac{1}{2}bh\left(2\right)\\ 2A=bh\\ \frac{2A}{h}=\frac{bh}{h}\\ \frac{2A}{h}=b\\ b=\frac{2A}{h}\end{array}$

Thus, the formula for the variable is, $b=2\frac{A}{h}$ .