A 7-foot tall stop sign creates a shadow that is 2 feet long. At the same time, a utility pole creates a shadow that is 11 feet long. How tall, in feet, is the utility pole?

Guest Nov 21, 2018

#1**+1 **

Let's create a proportion:

actual height: shadow length

using what we have, we make the ratio

7ft: 2ft, and the ft cancels out to 7: 2

next up, we set up a variable x. the ratio of the utility pole is

x ft: 11ft, and the ft cancels out to x: 11, like before.

7:2 = 7/2

x:11 = x/11

they are equal, so

7/2 = x/11

multiply both sides by 2:

7 = 2x/11

multiply both sides by 11:

77 = 2x

isolation x:

77/2 = x, and 77/2 is the answer

MATHEXPERTISE
Nov 21, 2018

#2**+1 **

The ratio is 7:2. If the pole's shadow is 11 feet long, we can multiply 11 by \(\dfrac{7}{2}\) to get \(38\dfrac{1}{2}\). The pole is \(38.5\) feet tall.

PartialMathematician
Nov 21, 2018