ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning
Study concepts, example questions & explanations for ISEE Middle Level Quantitative
All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #8 : Triangles
The lengths of 
Which is the greater quantity?
(a)
(b) The perimeter of
It is impossible to tell from the information given
(b) is greater
(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 #5 : 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
It is impossible to determine which is greater from the information given
(A) is greater
(B) is greater
(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 
Example Question #251 : Geometry
Note: Figure NOT drawn to scale.
Refer to the above triangle. An insect walks directly from A to B, then directly from B to C. What fraction of the perimeter of the triangle has he walked?
By the Pythagorean Theorem, the distance from A to C, which we will call 
The perimeter of the triangle is 
Example Question #251 : Geometry
Note: Figure NOT drawn to scale
Refer to the above triangle. An insect walks directly from B to C, then directly from C to A. What fraction of the perimeter of the triangle has he walked?
By the Pythagorean Theorem, the distance from B to C, which we will call
The perimeter of the triangle is
The insect has traveled 
of the perimeter.
Example Question #253 : Geometry
Note: Figure NOT drawn to scale
Refer to the above triangle. An insect walks directly from A to B, then directly from B to C. What percent of the perimeter of the triangle has he walked?
By the Pythagorean Theorem, the distance from B to C, which we will call
The perimeter of the triangle is
The insect has traveled 
Example Question #252 : Geometry
A triangle has base 80 inches and area 4,200 square inches. What is its height?
Use the area formula for a triangle, setting 
Example Question #2 : How To Find The Area Of A Triangle
The sum of the lengths of the legs of an isosceles right triangle is one meter. What is its area in square centimeters?
It is impossible to determine the area from the information given
The legs of an isosceles right triangle have equal length, so, if the sum of their lengths is one meter, which is equal to 100 centimeters, each leg measures half of this, or
The area of a triangle is half the product of its height and base; for a right triangle, the legs serve as height and base, so the area of the triangle is
Example Question #11 : Triangles
The above figure depicts Square 
Since 
The area of 
The area of the square is the square of the length of a side, which is 
Example Question #11 : Triangles
Which of the following is the greater quantity?
(a) The area of the above triangle
(b) 800
(b) is the greater quantity
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(b) is the greater quantity
The area of a right triangle is half the product of the lengths of its legs, which here are 25 and 60. So
which is less than 800.
Certified Tutor
All ISEE Middle Level Quantitative Resources
