The height of a pop can is 15 cm and its shadow is 20 cm long. A carton of milk next to the can is 0.25 m tall. Determine the length of the carton's shadow, to one tenth of a centimeter.
I did 100cm*0.25... but the answer is 33.3cm How did they get that?
Ah, the shadow mysteries of the can and carton! Let's shed some light on this, shall we?
We know that the height of the can is 15 cm and its shadow is 20 cm long. Now, let's assume the height of the carton of milk is indeed 0.25 m (or 25 cm).
To find the length of the carton's shadow, we can use a proportion:
Height of Can / Length of Can's Shadow = Height of Carton / Length of Carton's Shadow
So, substituting the given values:
15 cm / 20 cm = 25 cm / Length of Carton's Shadow
Cross multiplying gives us:
15 cm * Length of Carton's Shadow = 20 cm * 25 cm
Now, simplifying:
Length of Carton's Shadow = (20 cm * 25 cm) / 15 cm
And multiplying:
Length of Carton's Shadow = 33.3 cm
So, it seems like the correct answer is indeed 33.3 cm. Don't worry, math can be a shadowy realm sometimes, but we've got you covered!
To find the length of the carton's shadow, you can use a proportion based on similar triangles.
First, let's convert the height of the carton of milk from meters to centimeters:
0.25 m = 0.25 * 100 cm = 25 cm
Now, we can set up a proportion using the heights and their respective shadows:
Height of Pop Can / Length of Pop Can's Shadow = Height of Carton / Length of Carton's Shadow
Substituting the given values:
15 cm / 20 cm = 25 cm / x
Now, you can cross-multiply and solve for x:
15 * x = 20 * 25
x = (20 * 25) / 15
x ≈ 33.3 cm
Therefore, the length of the carton's shadow, to one-tenth of a centimeter, is 33.3 cm.
To determine the length of the carton's shadow, we can use similar triangles. The height of the pop can is 15 cm, and its shadow is 20 cm long. Let's use these measurements to set up a proportion.
Let h be the length of the carton's shadow in centimeters. Since the height of the pop can and the carton of milk are in different units (cm and m), we need to convert the height of the carton to centimeters. There are 100 centimeters in one meter, so the height of the carton in centimeters is given by:
0.25 m * 100 cm/m = 25 cm
Now we can set up the proportion:
15 cm / 20 cm = 25 cm / h
To solve for h, we cross multiply:
15 cm * h = 20 cm * 25 cm
Multiply the numbers on the right side:
15h = 500 cm^2
Divide both sides by 15 cm:
h = 500 cm^2 / 15 cm
Simplify the right side:
h ≈ 33.3 cm (rounded to one decimal place)
Therefore, the length of the carton's shadow is approximately 33.3 cm.
0.15/20 = 0.25/x
Cross multiply and solve for x.
20 * 0.25 = 0.15x
5/0.15 = x
33.33 = x