Question

A 40-foot tree casts a 12-foot shadow. How long is the shadow of a 5-foot-tall person?

Answer 1

Answer:

D

Step-by-step explanation:

For this type of problem, we need to think of it as a ratio.

The first tree to shadow ratio would be 40:12 this can be simplified to 20:6 which can be simplified to 10:3.

The second ratio is 5:x. I say x because it's an unknown number. Since 5 is half of ten, then the x would be half of three. Therefore the answer is D.

Answer 2

Answer:

$\text{D) }1.5\text{ feet}$

Step-by-step explanation:

We can use proportionality to solve this.

The height of the tree can act as the height of a right angled triangle, where the shadow is the base. The angle between the end of the shadow and the top of the object will be the same as the sun will shine from the same relative angle in the sky.  

Therefore :

$\frac{\text{Height of tree}}{\text{Height of person}}=\text{Scale factor}=\frac{\text{Length of tree's shadow}}{\text{Length of person's shadow}}$

$\frac{40}{5}=8\\\frac{12}{x}=8\\\text{Where x is the length of the person's shadow}\\12=8x\\x=1.5$

$\frac{12}{x}=8$