How to find the length of the side of a pentagon - ISEE Upper Level (grades 9-12) Quantitative Reasoning
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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
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
If each of the five congruent sides has measure 
, then the other two sides have measures 
and 
. Add the sides to get the perimeter, which is equal to 
feet, the solve for 
:
feet
Now we can compare (a) and (b).
(a) The longest side has measure 
feet.
(b) The three shortest sides each have length 856 feet; twice this is 
feet.
(b) is greater.
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.
Compare your answer with the correct one above
A regular pentagon has perimeter one yard. Which is the greater quantity?
(A) The length of one side
(B) 7 inches
A regular pentagon has perimeter one yard. Which is the greater quantity?
(A) The length of one side
(B) 7 inches
One yard is equal to 36 inches. A regular pentagon has five sides of equal length, so one side of the pentagon has length
inches.
Since 
, (A) is greater.
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
Compare your answer with the correct one above