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
To solve this problem, we can set up a proportion based on the given information.
Let's call the height of the tree "x" and the length of its shadow "y".
According to the problem, the height and shadow length are directly proportional, which means their ratio is constant. We can express this as:
6 feet / 15 feet = x feet / y feet
Now, we can solve this proportion for "y" by cross-multiplying:
6 * y = 15 * x
Next, divide both sides of the equation by 6 to solve for "y":
y = (15 * x) / 6
Now, we can substitute the height of the tree, which is 20 feet, into the equation:
y = (15 * 20) / 6
Calculating the expression on the right side:
y = 300 / 6
Simplifying this further:
y = 50
Therefore, the shadow of a 20-foot tree is 50 feet long.
To find the length of the shadow of a 20-foot tree, we can use direct variation. Direct variation states that if two quantities are directly proportional, their ratio remains constant.
In this case, the height of the object (tree) is directly proportional to the length of its shadow. We can set up a proportion using the given information:
Height of the person / Length of the person's shadow = Height of the tree / Length of the tree's shadow
Plugging in the given values:
6 feet / 15 feet = 20 feet / x
Cross-multiplying:
6x = 15 * 20
Simplifying:
6x = 300
To find x, we divide both sides of the equation by 6:
x = 300 / 6
x = 50
Therefore, the shadow of the 20-foot tree is 50 feet long.
If the shadow length is s, and the height is h, then
h = ks
That means that h/s = k, a constant. So, you want s such that
6/15 = 20/s