The height of an object varies directly with the length of its shadow. A person who is 6 feet tall casts a 15-foot shadow. How long is the shadow of a 20-foot tree? answer

6/15 = 20/x

Cross multiply and solve for x.

To find the length of the shadow of a 20-foot tree, we can use the concept of direct variation. Direct variation states that if two quantities are directly proportional, they can be represented by the equation y = kx, where y and x are the variables representing the two quantities and k is the constant of variation.

In this case, the height of the object (y) varies directly with the length of its shadow (x). We are given that when a person who is 6 feet tall (y) casts a 15-foot shadow (x). Therefore, we can set up the following equation:

y = kx

Substituting the given values, we get:

6 = k(15)

To find the value of k, we divide both sides of the equation by 15:

6/15 = k

Simplifying, we get:

2/5 = k

Now that we have the value of k, we can use it to find the length of the shadow of a 20-foot tree. Let's call the length of the shadow of the tree as x:

y = kx

Substituting the values, we get:

20 = (2/5)x

To isolate x, we can multiply both sides of the equation by 5/2:

20 * (5/2) = x

Simplifying, we get:

50 = x

Therefore, the length of the shadow of a 20-foot tree would be 50 feet.