To solve for the height \( h \) in the area formula of a triangle \( A = \frac{1}{2} bh \), we can rearrange the equation as follows:
-
Multiply both sides by 2:
\( 2A = bh \) -
Divide both sides by \( b \) (assuming \( b \neq 0 \)):
\( h = \frac{2A}{b} \)
Now we are looking for the units of the remaining terms when justifying this rearrangement. The area \( A \) is typically measured in square units (e.g., cm²), and \( b \) (the base) is measured in linear units (e.g., cm).
So, when you rearrange to find \( h \):
- The left side, \( h \), has units of cm.
- The right side, \( \frac{2A}{b} \), can be broken down as follows:
- \( A \) has units of cm².
- \( b \) has units of cm.
Thus, when you calculate \( \frac{2A}{b} \), you get:
\[ \frac{cm^2}{cm} = cm \]
This confirms that height \( h \) is indeed measured in cm.
The best response to represent the remaining units when justifying this rearangement is:
cm = cm
This expresses that both sides of the equation are consistent in their units when solved for \( h \).