Question

How do you use the area of a triangle to solve for B where B stands for base of the triangle?

Answer 1

Hint: We first explain the terms in the equation $A=\dfrac{Bh}{2}$. We find the particular triangular figure which follows the formula. We find their volume using the base area. From the values we verify the result.

Complete step by step solution:
The formula for area of a triangle is $A=\dfrac{Bh}{2}$.
In the equation three variables have been used. These variables have their own meaning for the figure. The variable $A$ stands for the area of the figure. The variable $B$ stands for the length of the base side of the figure. The variable $h$ stands for the height of the figure.
All three variables are just numbers. We can treat them as algebraic variables.
For example: in case of a triangle the base length is $B=4$. Let’s assume the height of the cube is also 4 units.

Then the area is $A=\dfrac{Bh}{2}=\dfrac{4\times 4}{2}=8$.
Therefore, we can just divide both sides of the equation $A=\dfrac{Bh}{2}$ with $\dfrac{h}{2}$.
The equation becomes
$\begin{align}
  & A=\dfrac{Bh}{2} \\
 & \Rightarrow \dfrac{2A}{h}=\dfrac{Bh}{h}\times \dfrac{2}{h}=B \\
\end{align}$
Therefore, the solution for $B$ from the equation $A=\dfrac{Bh}{2}$ is $B=\dfrac{2A}{h}$.
We verify the result from the perspective of the cube. Base was $B=4$. We verify the result with $B=\dfrac{2\times 8}{4}=\dfrac{16}{4}=4$. Thus verified $B$ is $B=\dfrac{2A}{h}$.

Note: We can only solve this equation in every case as the area follows the same formula. In cases where the formula changes the value of $B$ also changes according to the formula. We need to remember that the equation does not necessarily have to be a formula for area all the time.