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Question

Each side of a pentagon is 20 inches longer than the previous side. What is the length of the shortest side if the perimeter is 401 inches?


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Solution

Step 1: Find the sides of the pentagon.

Let the shortest side of the pentagon be x.

Since each side of a pentagon is 20 inches longer than the previous side, thus the sides of the pentagon are as follows:

x+20,x+20+20,x+20+20+20 and x+20+20+20+20, i.e. x+20,x+40,x+60 and x+80.

Step 2: Find the value of x.

Since the perimeter of the pentagon is 401 inches.

It is known that the sum of all the sides of the polygon is the perimeter of the polygon.

Thus,

x+x+20+x+40+x+60+x+80=4015x+200=4015x+200-200=401-200Subtract200frombothsidesoftheequation5x=2015x5=2015Dividebothsidesoftheequationby5x=40.2

Hence, the shortest side of the pentagon is 40.2 inches.


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