Final answer:
By using the principle of similar triangles, the length of Erin's shadow is calculated to be 60 inches when she stands next to the fire hydrant.
Step-by-step explanation:
To solve the problem of finding the length of Erin's shadow when she stands next to a fire hydrant, we can use the concept of similar triangles. The ratio of the height of an object to the length of its shadow will be the same for two different objects if the light source (e.g., the Sun) is far away and the ground is level.
In this case, we have a fire hydrant which is 32 inches tall and casts a 40 inch shadow. Using the proportion (height of fire hydrant)/(length of fire hydrant's shadow) = (height of Erin)/(length of Erin's shadow), we set up the equation:
32/40 = 48/x
Now we solve for x, which represents the length of Erin's shadow:
x = (48 × 40) / 32
By cross-multiplying and simplifying the equation, we find that:
x = 60 inches
Therefore, the length of Erin's shadow is 60 inches.