Question

The formula for the area of a triangle is$A=\frac{1}{2}bh$, where A represents the area, b is the base, and h, is the height of the triangle. Solve the equation for b.

Short answer

The equation for b is $b=\frac{2A}{h}$.

Step-by-step solution

Step 1. State the concept used.

• To get rid of a number in addition from one side, subtract the same number from both sides of the equal sign.
• To get rid of a number in subtraction from one side, add the same number on both sides of the equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of the equal sign.
• To get rid of a number in the division from one side, multiply the same number on both sides of the equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar signs always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of the larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similarsign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Step 2. Rewrite the equation to solve for b.

To solve the given equation$A=\frac{1}{2}bh$for the variable, isolate the variable term bon one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolateb, first multiply both sides by 2.

localid="1647505917733" $$\begin{gathered} A=\frac{1}{2}bh \\ 2A=2\times \frac{1}{2}bh \\ 2A=bh \end{gathered}$$

Step 3. Simplify further for b.

Now to further simplify divide both sides by h.

$$\begin{gathered} 2A=bh \\ \frac{2A}{h}=\frac{bh}{h} \\ \frac{2A}{h}=b \end{gathered}$$