An object's height varies directly with the length of its shadow. A person who is 5 feet tall casts an 8-foot shadow. How long is the shadow of a 20-foot tree?
5/8 = 20/x
Cross multiply and solve for x.
32
Right.
To solve this problem, we need to use the concept of direct variation. In direct variation, two variables are directly proportional to each other. This means that as one variable increases or decreases, the other variable also increases or decreases in proportion.
In this case, we are given that the height of an object is directly proportional to the length of its shadow. Let's denote the height of the object as h and the length of its shadow as s.
We are given that when a person who is 5 feet tall casts an 8-foot shadow, we can write this as:
h = k * s
where k is the constant of variation. We can find the value of k by using the given information:
5 = k * 8
Now, we can solve for k by dividing both sides of the equation by 8:
k = 5/8 = 0.625
So, the equation expressing the direct variation is:
h = 0.625s
Now, we can use this equation to find the length of the shadow of a 20-foot tree. We'll substitute h = 20 into the equation and solve for s:
20 = 0.625s
To isolate s, divide both sides of the equation by 0.625:
s = 20 / 0.625
Now, divide 20 by 0.625 to get the length of the shadow:
s ≈ 32
Therefore, the length of the shadow of a 20-foot tree is approximately 32 feet.