ISEE Upper Level Quantitative : Rhombuses
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
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Example Questions
Example Question #61 : Quadrilaterals
In Rhombus 
(A)
(B)
(a) is the greater quantity
(b) is the greater quantity
It cannot be determined which of (a) and (b) is greater
(a) and (b) are equal
(a) is the greater quantity
The four sides of a rhombus, by defintion, have equal length, so
Since 
Example Question #68 : Quadrilaterals
A rhombus has diagonals of length two and one-half feet and six feet. Which is the greater quantity?
(A) The perimeter of the rhombus
(B) Four yards
(A) and (B) are equal
(B) is greater
(A) is greater
It is impossible to determine which is greater from the information given
(A) is greater
It will be easier to look at these measurements as inches for the time being:
The diagonals of a rhombus are each other's perpendicular bisector, so, as can be seen in the diagram below, one side of a rhombus and one half of each diagonal form a right triangle. If we let 
By the Pythagorean Theorem,
Each side of the rhombus measures 39 inches, and its perimeter is
Four yards is equal to 
Example Question #1 : How To Find The Length Of The Diagonal Of A Rhombus
A rhombus has sidelength ten inches; one of its diagonals is one foot long. Which is the greater quantity?
(a) The length of the other diagonal
(B) One and one-half feet
It is impossible to determine which is greater from the information given
(B) is greater
(A) is greater
(A) and (B) are equal
(B) is greater
The diagonals of a rhombus are each other's perpendicular bisector, so, as can be seen in the diagram below, one side of a rhombus and one half of each diagonal form a right triangle. If the other diagonal has length 
This triangle fits the well-known Pythagorean triple of 6-8-10, so
The other diagonal measures 16 inches. One and one-half feet is equal to 18 inches, making (B) greater.
Example Question #271 : Plane Geometry
Rhombus 
(a)
(b)
It is impossible to tell from the information given
(a) is greater
(b) is greater
(a) and (b) are equal
(a) and (b) are equal
The diagonals of a rhombus always intersect at right angles, so 
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