An entrepreneur wants to rent a billboard at least 30 feet tall to display an advertisement for her business. She is 5 feet 6 inches tall and casts a shadow 7 feet long. At the same time, a billboard casts a shadow 35 feet long. Is the billboard tall enough?
To determine if the billboard is tall enough, we can use proportions.
The entrepreneur's height is 5 feet 6 inches, which can be expressed as 5.5 feet.
Let x be the height of the billboard.
We can set up the proportion:
(height of entrepreneur) / (length of entrepreneur's shadow) = (height of billboard) / (length of billboard's shadow)
(5.5 feet) / (7 feet) = x / (35 feet)
To solve for x, we cross-multiply:
7 * x = 5.5 * 35
7x = 192.5
Dividing both sides by 7:
x = 27.5
Therefore, the height of the billboard is 27.5 feet. Since it is less than the desired height of 30 feet, the billboard is not tall enough.