How to find the length of the side of a pentagon
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ISEE Upper Level Quantitative Reasoning › How to find the length of the side of a pentagon
A pentagon with a perimeter of one mile has three congruent sides. The second-longest side is 250 feet longer than any one of those three congruent sides, and the longest side is 500 feet longer than the second-longest side.
Which is the greater quantity?
(a) The length of the longest side of the pentagon
(b) Twice the length of one of the three shortest sides of the pentagon
(b) is greater.
(a) is greater.
(a) and (b) are equal.
It is impossible to tell from the information given.
Explanation
If each of the five congruent sides has measure 
Now we can compare (a) and (b).
(a) The longest side has measure 
(b) The three shortest sides each have length 856 feet; twice this is 
(b) is greater.
In a pentagon in which all the angles are equal and the perimeter is 35 inches, how many inches would be the sum of 2 of the sides?
Explanation
In a pentagon in which all angles are equal, all sides will also be equal; therefore, the length of one side can be found by dividing the perimeter by 5 (the number of sides in a pentagon). Given that 
A regular pentagon has perimeter one yard. Which is the greater quantity?
(A) The length of one side
(B) 7 inches
(A) is greater
(B) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
Explanation
One yard is equal to 36 inches. A regular pentagon has five sides of equal length, so one side of the pentagon has length
Since 
If a pentagon has a perimeter of 85in, what is the length of one side of the pentagon?
Explanation
A pentagon has 5 equal sides. We know the formula to find perimeter of a pentagon is
where a is the length of one side of the pentagon. Now, we know the total perimeter is 85in. Knowing this, we will substitute into the formula. We get
Therefore, the length of one side of the pentagon is 17in.