ISEE Upper Level Quantitative : How to find the length of a side
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #1 : How To Find The Length Of A Side
A regular decagon has the same perimeter as the above right triangle. Give the length of one side.
By the Pythagorean Theorem, the hypotenuse of the right triangle is
A regular decagon has ten sides of equal length, so each side measures
Example Question #3 : Other Polygons
A regular octagon has perimeter one meter. Which is the greater quantity?
(A) The length of one side
(B) 125 millimeters
(A) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(B) is greater
(A) and (B) are equal
A regular octagon has eight sides of equal length. The perimeter of this octagon is one meter, which is equal to 1,000 millimeters; each side, therefore, has length
making the quantities equal.
Example Question #104 : Plane Geometry
A regular pentagon has sidelength 72; the perimeter of a regular hexagon is 80% of that of the pentagon. Which is the greater quantity?
(A) The length of one side of the hexagon
(B) 50
(A) and (B) are equal
(A) is greater
It is impossible to determine which is greater from the information given
(B) is greater
(B) is greater
A regular pentagon has five sides of equal length; since one side is 72 units long, its perimeter is
80% of this is
so this is the length of the hexagon, and, since all six sides are of equal length, one side measures
(B) is greater.
Example Question #4 : How To Find The Length Of A Side
A regular octagon has twice the perimeter of a regular pentagon. What is the ratio of the sidelength of the octagon to that of the pentagon?
The solution is independent of the actual lengths, so we assume the pentagon has sidelength 1. Its perimeter is therefore 5. Subsequently, the octagon's perimeter is twice this, or 10, and its sidelength is one-eighth of this, or
The ratio of the sidelength of the octagon to that of the pentagon is
Example Question #4 : Other Polygons
A regular octagon has perimeter one mile.Which is the greater quantity?
(a) The length of one side
(b) 880 feet
It is impossible to determine which is greater from the information given
(b) is the greater quantity
(a) is the greater quantity
(a) and (b) are equal
(b) is the greater quantity
A regular octagon has eight sides of equal length. The perimeter, which is the sum of the lengths of these sides, is one mile, which is equal to 5,280 feet. Therefore, the length of one side is
All ISEE Upper Level Quantitative Resources
