what is the process for solving the following question?
John is 72 inches tall and casts a 40 inch shadow.
A monument casts a 24 foot shadow. How tall is the monument?
72/40 =h/24
so
h = 24 (72/40) feet
Change the inches to feet.
72 inches = 6 feet
40 inches = 3.333 feet
Set up a proportion and cross multiply.
6/3.333 = x/24
Thank you so much!
LOL
72/40 = 6/3.3333....
Ratio of height to shadow length could be in shoelace lengths as long as the same shoelace is used top and bottom.
To solve this question, we need to set up a proportion between the height of John and the height of the monument based on their respective shadows.
Step 1: Convert the units
First, we need to convert John's height and shadow length into the same units as the monument's shadow length.
John's height is given as 72 inches. Since the shadow length of the monument is given in feet, we need to convert inches to feet. Since there are 12 inches in a foot, we divide John's height by 12: 72 inches รท 12 = 6 feet.
Step 2: Set up the proportion
Next, we set up a proportion between John's height and shadow length, and the monument's height and shadow length.
Let's call the height of the monument "M."
The proportion can be set up as follows: 6 feet / 40 inches = M / 24 feet.
Step 3: Solve the proportion
To solve the proportion, cross-multiply and solve for "M."
Cross-multiplying gives us: (6 feet) * (24 feet) = (40 inches) * (M)
Simplifying this equation: 144 feet^2 = 40 inches * M
Dividing both sides of the equation by 40 inches: (144 feet^2) / (40 inches) = M
Step 4: Convert the units
We need to convert the length of the monument back to feet since we originally converted John's height to feet.
There are 12 inches in a foot, so we divide 144 ft^2 by 12 to convert it back to feet: (144 feet^2) / 12 = 12 feet.
Therefore, the height of the monument is 12 feet.