Question

Given the formula for the area of a triangle A=1/2bh which equation best represents the remaining units when justifying your rearrangement to solve for the height

2cm=cm
cm^2=cm^2
cm^2/cm=cm
cm=cm

Answer 1

To rearrange the formula for the area of a triangle \( A = \frac{1}{2} bh \) in order to solve for the height \( h \), we start by isolating \( h \).

1. Multiply both sides by 2:
\[
2A = bh
\]

2. Now divide both sides by \( b \):
\[
h = \frac{2A}{b}
\]

Now, looking at the units involved:

- The area \( A \) is measured in square centimeters (cm²).
- The base \( b \) is measured in centimeters (cm).

Thus, when handling the units to find \( h \):
- The units of the area \( 2A \) are also cm².
- By dividing cm² by cm, we have:

\[
\frac{\text{cm}^2}{\text{cm}} = \text{cm}
\]

This means that the units for height \( h \) will be in centimeters (cm).

So, the equation that best represents the remaining units when justifying the rearrangement to solve for the height in the area of triangle is:

\[
\text{cm}^2/\text{cm} = \text{cm}
\]

This shows the unit consistency during the rearrangement process.