ISEE Middle Level Quantitative : Triangles
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Example Questions
Example Question #231 : Plane Geometry
Which is the greater quantity?
(a) The perimeter of a right triangle with legs of length 5 feet and 12 feet
(b) 8 yards
It is impossible to tell from the information given
(b) is greater
(a) is greater
(a) and (b) are equal
(a) is greater
The length of the hypotenuse of a triangle with legs 5 feet and 12 feet is calculated using the Pythagorean Theorem, setting 
The hypotenuse is 13 feet long. The perimeter is 
Example Question #232 : Plane Geometry
Which is the greater quantity?
(a) The perimeter of a right triangle with hypotenuse of length 25 centimeters and one leg of length 7 centimeters
(b) One-half of a meter
(a) and (b) are equal
(b) is greater
(a) is greater
It is impossible to tell from the information given
(a) is greater
The length of the second leg of the triangle can be calculated using the Pythagorean Theorem, setting 
The second leg has length 24 centimeters, so the perimeter of the triangle is
One-half of a meter is one-half of 100 centimeters, or 50 centimeters, so (a) is greater.
Example Question #1 : Triangles
Which is the greater quantity?
(a) The perimeter of an equilateral triangle with sidelength 30 inches
(b) The perimeter of a square with sidelength 2 feet
(a) is greater
(b) is greater
(a) and (b) are equal
It is impossible to tell from the information given
(b) is greater
Each figure has sides that are congruent, so in each case, multiply the sidelength by the number of sides.
(a) The triangle has perimeter 
(b) 2 feet are equal to 24 inches, so the square has sidelength 
The square has the greater perimeter.
Example Question #1 : Triangles
Rectangle 
Which is the greater quantity?
(a) The perimeter of
(b) The perimeter of Rectangle
It is impossible to tell from the information given
(a) and (b) are equal
(a) is greater
(b) is greater
It is impossible to tell from the information given
(a) The perimeter of the equilateral triangle is 
(b) 
Rectangle 
Without knowing 
If 
If 
Example Question #2 : Triangles
Which is the greater quantity?
(a) The perimeter of
(b) The perimeter of
(a) and (b) are equal
It is impossible to tell from the information given
(a) is greater
(b) is greater
(a) is greater
(a) As an isosceles triangle, 
in which case the perimeter of 
or
in which case the perimeter of 
(b) 
Regardless of the length of 
Example Question #4 : Triangles
Which is the greater quantity?
(a)
(b)
(a) is greater
It is impossible to tell from the information given
(b) is greater
(a) and (b) are equal
(a) and (b) are equal
(a) 
(b) 
Example Question #234 : Plane Geometry
Which is the greater quantity?
(a) The perimeter of a right triangle with legs of length 3 inches and 4 inches
(b) One foot
(a) and (b) are equal
It is impossible to tell from the information given
(a) is greater
(b) is greater
(a) and (b) are equal
The length of the hypotenuse of a triangle with legs 3 inches and 4 inches long is calculated using the Pythagorean Theorem, setting 
The hypotenuse is 5 inches long. The perimeter is therefore 
Example Question #235 : Plane Geometry
The lengths of 
Which is the greater quantity?
(a)
(b) The perimeter of
(b) is greater
It is impossible to tell from the information given
(a) and (b) are equal
(a) is greater
(a) and (b) are equal
By the Pythagorean Theorem,
By trial and error, it can be determined that the only two positive integers that can replace 
Add the three side lengths to get the perimeter 
Example Question #3 : Triangles
An equilateral triangle has perimeter two yards. Which is the greater quantity?
(A) The length of one side of the triangle
(B) 28 inches
(A) and (B) are equal
(A) is greater
(B) is greater
It is impossible to determine which is greater from the information given
(B) is greater
An equilateral triangle has three sides of equal length; the perimeter of this triangle is two yards, which is equal to 
Example Question #10 : Triangles
Note: Figure NOT drawn to scale.
Refer to the above triangle. An insect walks directly from B to A, then directly from A to C. What percent of the perimeter of the triangle has he walked?
It is impossible to answer the question from the information given.
By the Pythagorean Theorem, the distance from A to C, which we will call 
The perimeter of the triangle is 
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