Question

The formula for the area of a trapezold with altitude k and bases m and n is A=k/2(m+n)

Solve for m.

Answer 1

`m=(2A-kn)/(k)`

Hence, option C is true.

Explanation:

Given the expression

`A=(k)/(2)\left(m+n\right)`

Solving for 'm'

`A=(k)/(2)\left(m+n\right)`

Flip the equation

`(k)/(2)\left(m+n\right)=A`

Expanding by applying the distributive law:
`a\left(b+c\right)=ab+ac`

`(1)/(2)km+(1)/(2)kn=A`

Add (-1)/2 × kn to both sides

`(1)/(2)km+(1)/(2)kn+\left(-(1)/(2)kn\right)=\left(-(1)/(2)kn\right)+A`

simplify

`(1)/(2)km=-(1)/(2)kn+A`

Divide both sides by k/2

`((1)/(2)km)/((k)/(2))=(-(1)/(2)kn+A)/((k)/(2))`

`m=(2A-kn)/(k)`

Therefore,

`m=(2A-kn)/(k)`

Hence, option C is true.