Question

Rearrange the formula to highlight the height

Answer 1

`h = (2A)/(b+c)`

Explanation:

Original Equation:

`A = (1)/(2) (b+c)h`

Divide both sides by height

`(A)/(h) = (1)/(2)(b+c)`

Raise both sides to the exponent -1 :

`((A)/(h))^(-1) = ((1)/(2)(b+c))^(-1)`

Rewrite using the definition of a negative exponent:
`((a)/(b))^(-x) = ((b)/(a))^(x)`

`(h)/(A) = (1)/((1)/(2)(b+c))\\`

Multiply 1/2 by (b+c)

`(h)/(A) = (1)/((b+c)/(2))\\`

Keep, change, flip

`(h)/(A) = (1)/(1) * (2)/(b+c) = (2)/(b+c)`

Multiply both sides by A

`h = (2A)/(b+c)`

Also I forgot to mention but the exponent (-1) can be ignored after you flip it, since:
`((a)/(b))^x = (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.