Solve the equation [tex]\( A = \left(\frac{1}{2}\right) bh \)[/tex] for [tex]\( h \)[/tex].

A. [tex]\( h = \left(\frac{1}{2}\right) \frac{A}{b} \)[/tex]
B. [tex]\( h = \frac{2A}{b} \)[/tex]
C. [tex]\( h = \frac{2b}{A} \)[/tex]
D. [tex]\( h = \left(\frac{1}{2}\right) \frac{b}{A} \)[/tex]



Answer :

Let's solve the equation [tex]\( A = \left( \frac{1}{2} \right) b h \)[/tex] for [tex]\( h \)[/tex] step-by-step.

1. Given Equation:
[tex]\[ A = \left( \frac{1}{2} \right) b h \][/tex]

2. Step 1: Multiply both sides by 2 to eliminate the fraction:
[tex]\[ 2A = 2 \left( \frac{1}{2} \right) b h \][/tex]
Simplifying the right side:
[tex]\[ 2A = b h \][/tex]

3. Step 2: Divide both sides by [tex]\( b \)[/tex] to isolate [tex]\( h \)[/tex]:
[tex]\[ h = \frac{2A}{b} \][/tex]

Therefore, the solution to the equation [tex]\( A = \left( \frac{1}{2} \right) b h \)[/tex] for [tex]\( h \)[/tex] is:
[tex]\[ h = \frac{2A}{b} \][/tex]

This method isolates [tex]\( h \)[/tex] by systematically eliminating other variables and coefficients from the equation.