"a 6 ft adult has a shadow of 3.6 ft. long. How long is the shadow of a 5-ft child standing next to the adult"
6/3.6 = 5/x
Cross multiply and solve for x.
3 feet
6/3.6=5/x= x=3
To determine the length of the shadow of a 5-ft child standing next to the adult with a 6-ft shadow, we can use the concept of similar triangles and proportions. Let's break it down step by step:
1. Set up a proportion: To find the length of the child's shadow, we can set up a proportion between the height and the length of the shadows.
Let x be the length of the child's shadow.
The proportion can be written as:
(Height of the adult) / (Length of the adult's shadow) = (Height of the child) / x
2. Plug in the given values: The height of the adult is 6 ft, and the length of the adult's shadow is 3.6 ft.
The proportion becomes:
6 ft / 3.6 ft = 5 ft / x
3. Solve for x: Cross-multiply and solve for x.
(6 ft)(x) = (3.6 ft)(5 ft)
6x = 18 ft
x = 18 ft / 6
x = 3 ft
Therefore, the length of the shadow of the 5-ft child would be 3 ft.