SOLUTION: A rectangular window measures 54 inches by 24 inches. There is an a = 14-inch wiper blade attached by a b = 5-inch arm at the center of the base of the window, as shown in the figu

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Question 832030: A rectangular window measures 54 inches by 24 inches. There is an a = 14-inch wiper blade attached by a b = 5-inch arm at the center of the base of the window, as shown in the figure below. If the arm rotates 120, approximate the percentage of the window's area that is wiped by the blade. (Round your answer to one decimal place.)
Answer by math-vortex(648)   (Show Source): You can put this solution on YOUR website!
Hi, there--

THE PROBLEM:
A rectangular window measures 54 inches by 24 inches. There is an a = 14-inch wiper blade attached by 
a b = 5-inch arm at the center of the base of the window, as shown in the figure below. If the arm rotates 
120, approximate the percentage of the window's area that is wiped by the blade. (Round your answer to 
one decimal place.)

A SOLUTION:

Find the area of the rectangle window.
Let L be the length of the window.
Let W be the width.

The area is length times width, 54 * 24 = 1296 square inches.

Find the area of window swept by wipers.
The radius of the wiper is 14 inches. It wipes 120 degrees. This is one-third of a circle because 
120/360 = 1/3

The area of one-third of the circle is 

We want the percentage of the window that is swept by the wiper.

[area swept by wiper] / [area of window] * 100 = [percentage of window area swept by wiper]
 percent.


Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com


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