Question

Rearrange the formula to highlight the height

Answer 1

Answer:

$h = \frac{2A}{b+c}$

Step-by-step explanation:

Original Equation:

$A = \frac{1}{2} (b+c)h$

Divide both sides by height

$\frac{A}{h} = \frac{1}{2}(b+c)$

Raise both sides to the exponent -1 :

$(\frac{A}{h})^{-1} = (\frac{1}{2}(b+c))^{-1}$

Rewrite using the definition of a negative exponent: $(\frac{a}{b})^{-x} = (\frac{b}{a})^{x}$

$\frac{h}{A} = \frac{1}{\frac{1}{2}(b+c)}$

Multiply 1/2 by (b+c)

$\frac{h}{A} = \frac{1}{\frac{b+c}{2}}$

Keep, change, flip

$\frac{h}{A} = \frac{1}{1} * \frac{2}{b+c} = \frac{2}{b+c}$

Multiply both sides by A

$h = \frac{2A}{b+c}$

Also I forgot to mention but the exponent (-1) can be ignored after you flip it, since: $(\frac{a}{b})^x = \frac{a^x}{b^x}$, but since in our case the exponent is 1, and $a^1 = a$, so there's really no need to write out the distribution part, since we just get the same fraction, after flipping it.