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.