Q13. - Algebra 1

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.

Step-by-Step Solution

Answer

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

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 similar sign 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 b on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate b, first multiply both sides by 2.

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

Step 3. Simplify further for b .

Now to further simplify divide both sides by h.

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