Question

A farmer is 6 feet tall. his shadow is 10 feet long and his barn casts a 75 foot shadow, how tall is his barn

Answer 1

Use a comparison to compare the height and the shadow
$\frac{height}{shadow}= \frac{height}{shadow}$

now input the numbers to the comparison, suppose h is the height of the barn we want to find
$\frac{barnheight}{barnshadow}= \frac{farmerheight}{farmershadow}$
$\frac{h}{75}= \frac{6}{10}$

Solve the equation by moving 75 to the right side, and we'll find the value of h
$\frac{h}{75}= \frac{6}{10}$
$h= \frac{6}{10}(75)$
$h= \frac{6(75)}{10}$
$h= \frac{450}{10}$
$h=45$

The barn is 45 feet tall