(SAT Prep) The perimeter of pentagon ABCDE is 30 in, AB = 7 in, BC = CD = 6 in, DE = 5 in. How many sides of the pentagon have equal length?
To find the number of sides of the pentagon that have equal length, we need to examine the given information.
Let's start by drawing a pentagon and assigning the given measurements to its sides:
D
/ \
E / \ C
/ \
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A B
We have the following information:
AB = 7 inches
BC = 6 inches
CD = 6 inches
DE = 5 inches
Now, let's analyze the sides one by one:
Since AB is given as 7 inches, we can conclude that AB is not equal to any other side length.
Moving clockwise, BC is given as 6 inches. This side is equal in length to one other side, namely CD (also given as 6 inches).
Continuing in the same way, the last side of the pentagon, DE, is given as 5 inches. There are no other sides with the same length.
In summary, only two sides, BC and CD, have equal lengths.
Therefore, the answer to the question is that two sides of the pentagon have equal lengths.