a traffic sign casts a shadow 6ft long while a mailbox next to it casts a shadow 3ft long. if the traffic sin is 7 ft high how tall is the mailbox
7/6 = x/3
6x = 21
x = 3.5 feet
To find the height of the mailbox, we can use the concept of similar triangles. The triangles formed by the traffic sign and its shadow, and the mailbox and its shadow are similar.
Let's denote the height of the mailbox as 'x' feet.
According to the question, the length of the shadow of the traffic sign is 6 feet, and the length of the shadow of the mailbox is 3 feet.
Using the concept of similar triangles, we can set up the following proportion:
(Height of traffic sign) / (Length of traffic sign's shadow) = (Height of mailbox) / (Length of mailbox's shadow)
Plugging in the values we know:
7 ft / 6 ft = x ft / 3 ft
Cross-multiplying, we get:
7 ft * 3 ft = 6 ft * x ft
21 ft = 6x ft
Now, we can solve for x by dividing both sides of the equation by 6:
21 ft / 6 = x ft
3.5 ft = x ft
Therefore, the mailbox is 3.5 feet tall.
To find the height of the mailbox, we can use the concept of similar triangles.
Similar triangles have the same shape but different sizes. The ratios of the corresponding sides of similar triangles are equal.
In this case, let's consider two similar triangles - one formed by the traffic sign, its shadow, and a vertical line, and the other formed by the mailbox, its shadow, and the same vertical line.
Let's assume the height of the mailbox is "x" ft.
According to the given information:
The height of the traffic sign = 7 ft
The length of the traffic sign's shadow = 6 ft
The length of the mailbox's shadow = 3 ft
Now, we can set up a proportion between the corresponding sides of the two similar triangles:
(height of traffic sign) / (length of traffic sign's shadow) = (height of mailbox) / (length of mailbox's shadow)
Substituting the given values:
7 ft / 6 ft = x ft / 3 ft
Now, cross-multiply and solve for x:
7 ft * 3 ft = 6 ft * x ft
21 ft = 6x
Divide both sides by 6:
21 ft / 6 = x ft
x = 3.5 ft
Therefore, the mailbox is 3.5 ft tall.