A 40ft tall monument casts a shadow that just reaches the base of a 4ft tall parking meter. If the parking meter's shadow is 6.5ft long, how far apart are the monument and the meter?

you have similar triangles, so use simple ratios

x/40 = 6.5/4
x = 40(6.5)/4 = 65

they are 65 m apart.

To find the distance between the monument and the meter, we can use similar triangles and proportions. The height of the monument is directly proportional to the length of its shadow, as is the height of the meter to the length of its shadow.

Let's set up a proportion to solve for the distance between the monument and the meter.

Height of Monument / Length of Monument's Shadow = Height of Meter / Length of Meter's Shadow

Let's plug in the given values:
40 ft / Length of Monument's Shadow = 4 ft / 6.5 ft

Now, let's solve for the Length of the Monument's Shadow:

Length of Monument's Shadow = (40 ft × 6.5 ft) / 4 ft
Length of Monument's Shadow = (260 ft·ft) / 4 ft
Length of Monument's Shadow = 65 ft

So, the distance between the monument and the meter is equal to the length of the monument's shadow, which is 65 ft.

To find the distance between the monument and the meter, we can use similar triangles and the property of proportional sides.

Let's label the distance between the monument and the meter as 'x'.

We have two similar right triangles, one formed by the monument's shadow and the other formed by the meter's shadow.

The height of the monument is 40ft, and its shadow is x ft long.

The height of the meter is 4ft, and its shadow is 6.5 ft long.

We can set up the following proportion:

(40ft / x ft) = (4 ft / 6.5 ft)

To find 'x', we need to solve for it.

Cross-multiplying, we get:

40ft * 6.5ft = 4ft * x

260ft = 4ft * x

Dividing both sides by 4ft:

260ft / 4ft = x

65ft = x

Therefore, the monument and the meter are 65 feet apart.