Question

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

Answer 1

Answer:

$m=\frac{2A-kn}{k}$

Hence, option C is true.

Step-by-step explanation:

Given the expression

$A=\frac{k}{2}\left(m+n\right)$

Solving for 'm'

$A=\frac{k}{2}\left(m+n\right)$

Flip the equation

$\frac{k}{2}\left(m+n\right)=A$

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

$\frac{1}{2}km+\frac{1}{2}kn=A$

Add (-1)/2 × kn to both sides

$\frac{1}{2}km+\frac{1}{2}kn+\left(-\frac{1}{2}kn\right)=\left(-\frac{1}{2}kn\right)+A$

simplify

$\frac{1}{2}km=-\frac{1}{2}kn+A$

Divide both sides by k/2

$\frac{\frac{1}{2}km}{\frac{k}{2}}=\frac{-\frac{1}{2}kn+A}{\frac{k}{2}}$

$m=\frac{2A-kn}{k}$

Therefore,

$m=\frac{2A-kn}{k}$

Hence, option C is true.